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SOLOTIOIS AMD METHODS OP SOLUTIOMS K)R PROBLEMS MCOUHTERED 
ra THE THERl^M, DESICT OF SPACECRAFT 



By 
Richard E, Turner 

Thesis subnsitted to the Graduate Facxalty of the 
Virginia Polytechnic Institute 

in caadidacy for the degree of 

MASTER OF SCIEICE 







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AEROSPACE EMGHEERIHG 



May 196k 

N?l- 72251 



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(ACCESSION NJUMBER) 






(THRU) 



(PAGES) 



O (fvSASA CR OR TMX OR AD NUMBER) 



(CODE) 



(CATEGORY) 






SLacksiburg/ Virginia 



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B< Bi^i^mti^i^ of tb0 B^Hation fsrat^f^ l^i^biaii « # 



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f » Bjs^ei^SJLmtUm cxf tlifi Qe^t lqpmti<»x to ^E^tee- 

@« A Berametaeie @%(ias;f of Ozibltel Seating 

B* Se^v^yum fmr ^Im MmOiixmat Beat Eg^gtetioii . . * . 
I* iaototi<m of t^ Best Sftze^ion for Spaceoraft 

&vtB@ IMfbsm *£e8i>eir&tux«s 

J* SQl.ut£<8i of tiKl iSs&'t Bqpmt&OiQ fi»r a OslixxBriceH 

S^umm&St WLiSa. WLob Se^eciiest Sesiipeiraiture 

Bemainwair Sotn^te)^ Ooctdittons ......... 



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t« SSsttiii J^stlUiiyjig m teii tci % Via«@^ (1^ ^ ^ * « . « « ^ « 129 

€« itel^ i^b^oi^y^ a Hat Wt^m Belali^ ^ Itis lar^ « « • X55 
T* i^t%^ ft^i^di^ mi ^ht% M.mm ^ ite ter^ . « ^ « • • x^^ 

X0* l^sat^ ffltoilJ^ ^tii^^^^aX Bs^ar 0ia^€li»fee l^«i© * . * X37 
XX » €lte1^ BeXaMii^ s ^i^f&i^ BX^^i^i^ Wi ^ ^^Xiii^jf %0 

1ib# &rtib is^ Sim «*«*i«««»*««p»«4«* X33 

X2* ^^%^ ^^^liag 1^ M^Ki^ of a ^liaXX's Syyrf^iM^ « « « « * X^ 

X|^« Ji?^ijt lijit^tatigia £^ C^s c^ Virion KLf ^^ImB « « X^ 
X^# &rlto B^i^^ 1^ j^bedo IQ^at m a P^t ^i^^na f!ia$ 

WL^i^^ «*jifiit*»«»t»«««*** «»•<!»♦♦♦ X^2 

X€* f»|N6ra^ly0» IKtot Msim^ mi a flaa^c IXo^ With 
XT* €i@^pidli^^^ a^f Wm/^ ^iMtlmm MiM %pii»£tMa^ 



^^IniIjs^ l!r€m fUj^t M^ ^^ ^vmA Beetle 1^ 






.6. 

agf^rii:^UB will trawrse 1^ dSstaaeea ^fa^'mi^ mi eMXe^a boatlle m^irlra^ 
litirt; of i^paoa* ^0 of ^^ wm^ i^oT^nA a^et^ of «te m^vlTox^^m, 

&^i<^aiyi^ t^iipratore ^«trol0 hmm hmm ^mlm®& aloi3^ tw 
liaes, isfc^ l^gs^w a^/or tt»^ actl^ ttoerMl «iiitrta» Of coiirst> ttie 
i»i^^Dd0 of passim t^imal tef ipt i^r 1^ ijQMC^^:^:uted tmto aa a^tiire 
tliei3»l fetlpi s^4i«ia# It 10 iplM eidLS@ii& ttat ^00! w t@ffi^i^tm*# 
ecmfa^ i0 a<M0^^^t at 1i^ ttoei of <^3f^teuetitm <^ ifej ^M^eraflJ^ ^^ 
%y i^te ^p5^i<^ticm of pTi^^r q^cwal eoiitii^0» mX^etUm of tproec^nffe 

otSter iMfflftt a^ctlv^ Iti^xB^ ^mkim^ m§l£3^B tea* g^»rati^ a^^me^ 
i^fH^^ratio)^ ^vlmsi ^na otteer aluUw ^^-^rti* ^ role of paaMw 

^^ ^ille i^m aettw i»ttiOd i^tesAt be t3«td c^eOy 



At i^^aeat ia&0 »^Hiar^ mj^mmtm£% 1$ a Mall% m& its en^lrom* 

m^ ^m mUmU^ boftiee i^idi ao^imte the teat traa^sfeirecl to a 
spa^c^^i^ift ^ir^ tli0 0aii^ ^i^ sue* ^Sto dossdJia^ m^# of tn^at 



TeG&i^mB ^&t airectSjr ttma. tib@ bw& an^or ear^i e»d is Seated 1^ ^to 

SKtari! are aangr ipipdrt a'wsiXsMe ia ^be Xitearat^ure -Krlti^m <m 1^ 
^ears»l 4@eigis of ^^t«^enyn>» W^mtimBi^l^f e-vm t^bnugpbL the sa3>4ect 

me mmLiytUe^ m& %a.md i^^ler mmm^eem too rl^;ia te iNn c^ f^eeersa. 

ix^Tmt or to petslt an i^mi^t i^fee ^be pnMim its^af . 

of '^^sris^ eoi^foX f9ns^@90 ii^^ axe gesez^ is ae^^as^ ^binaewr tSbie 
Is p»e@lia«* Iten tlij@ pieibO-esss mmom^^exi^ ao aerfe ii^xslt eesersl 
soltxtdoa® tc> IN oMiali^ ilbeir mf^s&a of »sa«U(m aire p^&^ted im 
sttfneleiit itetall to pEtr«idto tD® 3«aiaer vl«h eamii^ "too3.8* to boImg 
r(»X«l»d t^nP^s o(f pif(M«$B* A |tsr«aa»trle «rt%i^ o^ orbital beatlag ^^dti 
x«^)ws 011X7 ® sdJQisnaa lcacnd«%& of oacMtaOL varisSaes is given. Shie 
dearls^ sltows t^ fiature A&d eoynseo of orbital heatiais* 



m- Q m 

p 

^^ ar^a of boiy (i) :p^4^cted to feo^ (j), iat 

^ m^a of §mmr^ bodly pr^Jeetea to bc^ (l)^ iaa*^ 

a^^ 4 $Smorp%iKm of radlaMcm from bCN]^ i t^ fec^ 4 

a^ ^sorpticm of imMatio^st trm^ ba% i by a ^wbtbX bo^ 

B0 a^i^ betPii^^ (mm) m^ "^^^^ ^^ 

% cotftitient fron i^xpa^Ptai^m C3€ 65 

Ci »tffleiismt fi^«» mm^mltm of ^ 

%*^% ^%* ^^* motels ^5M<^fS»m a rigbiVlmiid c^rtlio^oMl 

o girteBljsyii eqcgt?^&iBa^ frmm ^mmd^^M. %d^ the tth 
€^^03^illBat^ ^fw^^m. 

tmtt wister at tSte eej^str of Ite spac^^smft pointing 

S^.3^^^%^ <^)tfi^ai^iti la '^b^ ^i^sa^l^m of %(t) 



f^lXiBg cmto a j^NieeofEft 



. 9« 






JtattMi^ ©spe»t£% ii( ^ae iM9l%yj@» ef tdyae-de^ni^t 



% f^itetlati @$i@^Liig is ^^ sototicsa of tliae«il^?^Eiaent 



S t^emaisa mnHsmm'Vi^, BtuMa la. % 

%^ iixm iM mxtM0A pear ot^it period, acta 



* 10 * 

Wg ^^affi^mnt $m ^b m^^mMijtm of i^^ar im^^ cm a 

M^$\ fmmjkimk of X in ^ t^^qparal^^^ soXiiMc^ of a bc^ 

» ii@^t W0^^ 3i^wa. to a 0»rf^g^c^ 

f p^K^r par vM.% "^P^wm i^mtim^A in a Ik^^ Bto/Mn « In*^ 

Q rolmtii^ »t^fii£ 

Q teal; e^t^ of a 1:^^^ B^ 

U^ fBXw^mmi tetw^a^ raiiaMipg l^^diei^^ j^les 

% eart& ti^edo (0*4) 

r i^^tial €oof€i^^1^ Is ^i^i^rioal polar ooor^iia^a^ In. 

M^ T^^LWB of 0€t:rlli^ iidLX0s 

M M^B'bBisisus^ t^^niSE Tadiatin^ bodii^s^ niXes 



S iolar ]maiatiati a»0ti^^ Bto/ia*^ • ndLiii 

f I* the r^ ^S|p0a«te^^ patrteefeatioia^ ^ 

t0 1^ eartbtstm lim at tte tia^ of tlbi@ mmmr tola^m 
tbe ^Mt i^ai^ m^ l^ie 1* a^le ^imoMli^ viiM iAm 

X*%1*'^%'' ^o^^iptg^ar car^Bim 0!^ra*ii«*e trmm ¥li*t tlm T' axis 

.0aiBi2d^^t to t£i^ 0^^r^p>#^ Xi$^ w& W:^ 2>^ 0^^ 
pcii']piss^3ieiiiar to tte elliptic plaj^ 

%i%f% i^etaa@ilBr o^iH^siam ^rilBate trmm with tte % aada 

ot>liioSJdLi^ idth the aj^Ms^craft a^a of rol^tioiml 

^^ii^iiei^ to tli0 sa^Ui^^-^earl^ Xim ^^ 1^ & ^^^ 
I^iPig iB ^^te pJLi^i0 £ai^3»4 l?3r ite S^ mis mi0. ^m 
satellite *i 0^ wefeor m 

o^ ttemi aimai^ir, ^^^^ 

l^m mm^^B mwtfmm relatt^ to tte sateJLli^ m&^poiii^^ 



* 12 *» 
mk '^ mm^W^M mmf^i^s^ ir^al^w to 1;fee mm^B m&^^im^g 



i %ijm ^rii^tii?^ of orMt a^e^ rafliai^mlB 

£ s\m*0 l^g^t^;^ i^el^l-w to orbit piam dooi^iuat^ 

^0t«m y^^ Ite j^»i^t l^stem j^ C3P| deg 



9q liMt of ii3rt^gratiom of poAar a^Ie in 0p^c^a:^yrt*0 

^ li^tiBl. H3igl0 to0%p^©s oi:^it jt^sril^^ and ^B^is^Bg no^^ 



ih>h^^kr) test rat. mtioa 

A ^^@4w;1& m^^ in ^XiaSrical ^lar coc^rdiid^^^ allied 

w p!^4eietti »©^ of bc^ iriltto xmit surf a^Jt arei^ to ©horb* 

t@fm m^irn ^i^^ji iJja€^i^ic^000 

II pra^#cH^<^ ^rea of l^(il|f i4th mit mstfwo^ area ia la^« 

^tm BfiM m^m^ dii^ii^lc^esa 

? «itt ^wet^r £rcm ^p4»a?aft*0 center pointlxig to idei^r 

¥ latitude 0f ^^.^cs^^rft^a i^in axta (B) t^ati*^ to airtolt 

I as^ia ^p^il^ i^ 6pt^^^mft*s mdLB of sxitaticmal i@;pipe%ry 

Pii a^ term <^ the ^^ftet fsg^eliig faction, Bfei/te.® * Mja 

U^ ^«.t^c r^.*l« inten.1,^. Btu/m.' • ^ 

#1^ * total totat fl^sjt cm Ik:^ ^ fr<» is^r i, Wm/min 

^l ^ J tort^ heat te^ii0i1§r cm bo% ^ f*c» bofly 1> B^/lii*^ * i^Ln 

|j^ initial angle bet^^en X axt^ and asoaMiisig i^4m of orblt^ 



mm^&Sm^'is® B^f^ima. ^tb s@rl^^ takm as 4m/2f dfig 

f Isrptst dilTex'sawse Iseteeen {^) sad ^ 

t^^ ctiR^es; ftiiietl<m of X is tlH9 s>oOLu1d{m of teBsgpexm^ore 

«^ «ga«at rate is t^^, T&Sjt&, 

Q rni^mmi^ v&^ in tl» eai^^siasiem e^ lieat rates tm a 6x>ac%cxiilt'j 

a «mi.t ^meter ooin@idl»@ idLtb ^e 0pi& sgKle of the ^gta^E^cxiaft 

Cm) mit m^^m- mimimjcm i^tfo tbe fods of mtati^oaX 

spntttsy of tte epskcecraft 
(lil} unit wctor cotociSiag nitb the satellite" sim line 

(e) uait wetfGar eoiiieiiliag vith ^e satellite-earth line 



Subscripts: 

( }^ imsa mlfm vith ams^ct to time 

< )8mff.aiaaE ««iw» swrfaee nXm 



( )-- equilibrium axotition 



Wsm Bi;^o^ of Wm tMximl ocmtrtal of apaogentfb 1© a stoi^ of lieat 
traxi0fter^ ^fyav^ %}m ^^mmlMg e^iiatl^a^ e:^ii^saail tn -victor i»tatlcm 
Is (a^e T^f* 5) 

^ * ^ # p «. pe ^ (l) 

V is tt^ ^«etc>r #il 0^i«teor 

p is the beat orea.'^i in t^ mti^rlal a^eting bb m Mmt c<mMe%mr 

p ia th^ d^naiti^ 0f 1^ material actlis^ bb a teat <xmancl^r 

c l0 tha 401101% 0f 't^ 3g3iatt:riaJL aotiisig as a l^at conductor 

f is ti^ t^©ei^tiiar«s of ^^ i»terlal actii3yg aa a heat coaductor 

m^ 

% l0 ti^^ 

% l0 tte ^rmal e^^i^etl-^^ In tlia 1th dlrectlcm 
Xj^ is tta^ <^>oi^iimt© asaignad to t^ ItAi dlreetlcm 

Ie woi^ cashes e^patloa (l) cui^^t be ©ol^red ^ttout i^eo^irs^ to miMr« 
leal tedmlqiws* Wmn i^toa m^im% 0olutl<m0 to tte eqpatloii m^ a^vailable^ 



* l6 * 

TOSUit* flP3^ as a begtoiQd^ e^uatlcm (l) vlll "be ^^cialiaed for 

A first lii^rt^^ speeiailEatloaa -^lll be to fiM mi c^^greaaioti 
®i0 c^m fee aiC^oisgLlalied'by liatt®?atiag e^^atl^i (l) over 1^ lK>dy to 



' ^ dA 



^^A ^A ^A ^* 



appne-^r^ fey mae of the ftitei^m^ tfeeoi^sm tt is rteognlsed that 



/ ? • f3A t!. . 5 * t^ ^ f (mt teat ^sorted 
^A ^S per tmit time) 



( fM 5:s p {^Bt beat cwal^d Internally) 



m^ 



vbm^ n is tlit msxtmm w^% normal wetor ^d ^^ script f ia 



i^i^o^t far 



1 



flma i^ ^f:^f^it4iil ^^patl^^ ft^ f a ^^ 



1^ ^ F ^ * (a) 









* 7 • f-, * B « P€ c* 
^ dt 



^ «* ^ /net %\ fe 
y^ve Y is the filMlX wall IMetoess. fliae titore I^qIXows 



V ♦ '5y ♦ ^ ♦ p » PC ^ (3) 



la * 



©^ pp^^dT ^fm, ft is ffie0«fet m£ly for tl^ie l^^^a ifetor# eleetriaal 

i^cstii^ fy*m^ ti^ mm (liefla^ted ^ tl^ #»tti onto tte spweorsrft (aS^li^da) )# 
aid rB&im.% i^nmr 0^%t@a bjr tte eartb. Bie ealiJailaMcm of % i0 

ii^yft tg!N f%f^T'^ffiif^ and pi*0i^^t0 BO t^^^ratioiQ. 4i!ffi0iil't^| toi^i?i^i*^ ^ten 



B* Itefl'vv^liliCKa odE* iSmet Balliftlaaei ^Kraosfter B^ustloa 
Hfem 4«*^?.^iyifffffn% of x%alisrl»le teduil^Eaes fc»r calculatiBg tlie heat 
Hux ea a apted^rttft »ifit "bf^g^M lAish tslus tiidXolcaoim eacpreselcm for tlw 
ir«iiiax& pcwer exi^mi^pd tKf^MNSin tiK» eleaEattal asreas radiatlzis to «ac^ 
o«te»Tf fext IkkiIcs «n luMat treoKRiwr lore sooetiaes gailtgr of lewdlng tlie 

oiptraiaipatifiea. mm. ie ssmtmiteS to the xea&sr, Ooaase^uently^ tbe 
"dlfftiite" «ad "i^^eeiaiiEr" msdiatloa scmetJUDes are (^cOy vaguely 



a singLlfl9d diezlval^cm of thft classleal radiac 

tJjCM3> ]i(BMt*tx^8i3S]^4r a^^pafeiosi iA pi*isi®>eQtd&* !ioo^ tlii.s cterl'vatl<si eaa 



* X9 * 

1^ H^m It ]0Mm f is ^m@i4^r0& to t^ aaa JUtifliiif^ ipUm^ eon*^ 
^tinlug 1^ itla^si^Elal area (4^)1 ^^^^ elasiloaU^ ra^a^a 1mm% to 
(4%) * Tb^ »Mlla^iig w^t^riiii is ^o^sp^S €M its upper i^orfaae %^ 
^mm f %q.t i^ f^^y^^r^ 1^ l»e lufli^ilt^ im ^^dsemt m tl^ I^ne^r bcioi^ii 
tte radlai^^ im^ mti^i^m^M :^^m iM&t^, Ite ^€^@^i^taX toXiiik im^rmdL 

€bi0 ar0% (i%) jp@B00 a:^ai^at liaat It^^ i^ eX^t^nl^ ^cilt^^ 
(OA :>9 Mi&X^ to Ite eXMy^n^X gp^ea {M^) » ^te area (d%) Is c^^^sen bs 
peir^isyllcular to tija i^ejat^r liii$ ^^^i-^^^^ ^ *o dl^* 

^1^ raMating mat^:lal i^tlf radiates liast tinl^^^O^ im all 
Mrm^timmi^ fwm ^Qil «i^f^<^6ataim^ poii^^a* Ipi^wr^ aA is 00 a^aXX 
it 4mB not aifi^ieii^a^ TBis^m^h ita 0^ rMiat^d aiiei^;^ « 

M% iSm fmrnr md.t%&^ {p^r tmit m3^i»a) 1^ aA be |0a* ®^® »^* 
1:^ j^iir^ill^ ai^^i:ii^^ a# "^m l^mt trantla mti^ f^?^^ (4A)| ai^nriae 
t^ li^dia c^a^d licit mSli^* %i^^ 0^ is nc^t ^ oc^Eistcypr&i but 

litere ^^{t) iB ^^to beat &im pmr vmit m^^% m% a ^ati^^^ i* ^om its 

^mym %b wb db^i^bii^ i^tedia beli^t^m &% sad 4&g> tei^ all nm 
beat £rdi^ dA| 13,^0^^ 1^x^x0. M^^ idll si^aeb d^* Ai^ a dir^ret 
e^^M^^p^iOt of tbia 0ta^^^ 



^ « 



Cs • %l^t4(3P • s - %) » (a)^«iA(*' « a) 



car 



^(y «, 8) „ '^^ ^<r «. a . %) 






^ « (^•^^) «<® - »i>*^ 



B@x*e f^ is l!te %<»tal rsMaxrl f€w$r per iaal.% etarea of ajkg iaeidcmt oa 
4% (fxtm A) passing 1liii?mi|^ 4%. Mm ti&t^saeMsQ to t^ sleets 

418^ a eos 9 4B 
Kow^r 4elisdLag 4^ as 

^ «* 4Jigf--.Z-Skj ^^{t w H • %)^(^) cos 9 4B 

03B& 



- a 






@0v Mt (b * %) m Xg m ^M 






^0 



Btmm iM.B I0 a teflM^t^^ iittegraXt ^ycMSrn 



tg « ^ > ..n„.v:^,^. . 






i^f^ 4^ > r^ads: ^te air^a M^t 4li^ f^^Jeets oiitc^ iA^^ then 






1^ gtiiianti> i^ i^6i^ ^»dieB (1^4) , 



* ^ • 



%t-k^^^ <^> 



fte €^1^ ^y^seribetl i^^attoa la said t^ ^r^^ate diffctaels^ £itm d^* 
i^ilii#$^rf0d AriiL tilt e^r^ td^ a B^m^^^mtt^ tlm pno^e^^ted aas^a. of the 

^iiBlOy it^mA i^smm^^ airamg^a) ocima aaimd mlcmg an axis of 

ipu^ to mMmm ^fm^^ stiMIi^^* 1^ temoat t^ p^oad is Is^eeted 
into 03:%it tstt^ lE^iia f^sii»I eg&ii* £Pi t^ ai^^^^s^:^ of etrcmg exte»^ 
torgp^s tito @^p^i^l^ft^s 4aiiigul» wsKlxtaei i^ate^ vlll aippec^iro.^^ 
mato^rf^ a timBiSk tli»etica relative to imtrtial 0^00 ♦ If lite B-pam-^ 
is^mft is Bot |Nti^0t^ ri|^d ^»e ai^#ilar Mi^tie ^narg^ m^ tm loat 
t*i«s^iii^ stamet^na viiteratioiis^ f artetouXwlr i* tifct spiit mis Ib an aada 
ol^r Wmi ^mt of tli^ largeBt 3S3a^^iat of ii^^Hyia* JMSbt ^iiie ccmditimsi 



. 25 - 

tlie &]^mm&i%*B @0k& mis «aiX Vemmte^, la ^oras! fi&il^ u^se ot ti»ej» 
1@ t^ mdL& hmim t^ 3j!rg»st siW0&t of Inertia. 2^ ihle l^iesis It 
will Ise m»mBm&, Hy^ Wm IMMal &sda aade is ti»t of rotad^lonaX 

^mmii3A&A ^iffiRi^ wad s^ ^te «£U of Xsratst aoracmt o^ laeartLa. 
IMtiiUL spifi Vila. ^ ir^f^fed to as ttis ^'leAort texm splu laoaei" the 
£UsHii s|Kto m£^- ^Oi be j»£lsaT«4 t«) m tito "limg 'Nsca ^^ &od9«** 
1^ tMs £>ea0«m ^te inraJeetecL ®£>e@@ £s^«eti<»a@ of t&e &ms mast be 
liivesti^ted A$r ^itn iA»mit aa a«i@ of efmasttaEtrnX ^fomtrr loaSi eH^ 
Hg^ i^a Qi>ou.t an i@ils peirj^^Oi^oiil^f to the oxis of geKSHitfioaX 
^^netrsr. Xt is t&isit3^ eis@«^ed ^lat intexiwaiate 0piii sodes are 
uaiBl^rtffiat to tkm -Wimm^ ^sign of a i^E>Qs««»iKft* 

M(»0t spo^eraftf %te^ esdli^xi^d s«rf!»s»s cnxaaeit l}e s^s^ioaJUy 
i^PfToxtaat^ ^ a i@ifie@ of m^i&s, m& ^ ofitleaai^ re^ar«S)^siteA>Xe ty 
a mvia» of mama {iS Ite spbsteeraft sj^iias fast exxm^ eo lOiat l%a!s>era<» 
tw« HuetaatitiNos oinetr (xma %iiii oyde e«a l»e BegXoeted} fiEo* tbe pur]p>Be 
c^ osXiinilatiDig httat dusc (Stt tiie fl^paeoeraft* 

la tUffxm Z ^ ie w^ vHjmmxtal maSmt araa for a &xab of balf 
angle &4 Bui tJUnnatel. ar«a> SA^* ^^ ^ewad along t^ unit ^etor 
V, B i« tlie KBait acxsMl'wotor of diA^* Slius 

IHllil® 

S « %,j(eo8 & 008 7) # et|,(<»® * 8^ 7). ♦ ^(sin 8) 



^ 2h m 



|f m m^{BiM %} ^ ^.{€500 t|) 



mhmm Urn 0|^ mm w^% wetor^ tm Wm ilSi iii^etiatis« 



M^ y, ^ in * ^ 



♦ ?) art itoietet fiim the tetegr^M^* ^tois^ fw tl^ ecme^ 

mm ^ ^i^m T^ sin % * ain & ^^m r\ ^ 
iM^ 40 pOfi^BiMe if mA oily if 



^^0 S 0iE t| > 0to d 000 n (6) 



fQ^n If n<§ 
Tq^ If n > I 
If ##ii&tioi^ i$) ^kmn MM -^mn 7q i@ glwn 1>y 

cc^ Fq ^ **t^B cot n 

Ipw^ tl^ t0t^ l^i^sf^ area of ^be cosf^ 10 

^^n) «^ ^^n) '^ I {(00a d Bin y$)eiB n #0^^ tin d)c^a n^ (7) 

^tj) » €K>s^ (flat slate^ d « 1^/2) 

Tfm 0^mr aaie c^ to^ir^Bt I0 ^ mmB0& area pi^eis^ted to lam 
irtewir aias« v, Isy tSte ^^me^ «^ It roitetes {mm we^mlntlKm) ©Jxmt an 



* 26 • 



U^n) ^ (^ J i^Cn>l)&l (S) 



of i^MM^i Wit % i0 Mie i^^e t^i^^a^ V to (?^ » fl^ire 3 BTm^m 

^^^. g^.,.flffila^-- -„g^f f»P^. m^m*^ A 3;*^^ circuit €^i» of half 

ttes^ aal.titidiis« 1^ praje^tad area, of 1^ ccm^ in bo^ ^in w^bb^ 

tlie ^^0 ^ i^^w^l^i ^iis tenst eaJLeul^l^ for mmiB k@lf ai^i^s of ^^ 

jlo^tet ia fipii^a 15(11) assA 15(b) * 

&» daO^mila^c^ ^ ^teS^ ant &prth Wim^mO. Utatljaig 

(alb^qi) f0»r is ttwi#i%fte«iErt# 1^ mm^^ eqi^dla*do3Pi of s^iush 
4rta iter ai*>i1^a£«lJ;r Sfc^i^piA to^ai^i^ ii^iul& ^ a ^L^pt^tio te^ ewu for 
m^iim iigl^O. ia;»piterf # 1^ 1M© re^^Ei i^-mrml series solutLmia 

mcw^m^ ^pp^idaaticms for ^tii ^mr^ i^b^^rmal rad albe^ li^atli^^ of mn 



m 27 * 

earlii^s 0iir^m lid^fa tranasits T^^ms^ pcmer 1^ tlit si^eecraSt) * flits 
angle la w^mm:^^ i^cw^ ^be ]^^ 2| ^3umm irM^h (alse) ocmt^i^ tbe 

txea of ^te @pac^ei^yf& Is alig^^^ »f^»t3i^®<^ to tife uMt ^wctor S» 
fhe folsr a»#e of ^ tHat Is, t|^ Is t^ aagXe l>et»eem 1^ nm^ 
satellite lii^ 0M % l^g^m ^^te % assis ccdiKil^a tiitb t^ esprit 
Bi^llita li»» la IMi o«»rdtimte fSri^ia eiuatlcm (h)^ after Integr^^ 



^l,Y ^ (^) ^ ^m4n)^i3Pt 9 may (9) 



r^ is "^ytie ]^rc#ii% of tJte t^tenn^ SM^gy (l^p» IS10 sun 0M. Ixioide^t 
0^ if 13m i^mt^^mm mglm of tte mm^B light cm ^i# esrth^a Xoeal 
bo^ are ewn f^^%$mi@ tif n ^^ Ja^ 1^ vmpm^mhi^^ ^ a ooaim seri^t^ 



« 88 



4^) 



) % ews m 



Sin) » £^^ main 



¥ith liMrSe e^mmtions i»faatl4»n (9) beeoeses^^ after tnterghawgla g 



h,y - ^""^ i Z ^'k ^g ^i ^ fen «ia 8d9^ 
SVtM figure (%) It is evident that 



V « ^(ai» « ws y| ♦ IW(sla t ^ji y) ♦ ©^<©os 9) 



(10) 



^Di geoottry isfiiid^ (la i@ Bhmm in fignre ^. la tbe sicetcli 

diataii@e % (li^ Slstooee f^ra® tte @«,temit@'@ eeitter to the @ar1^*s 
^mter) to f^@ilita^ definlti^ 0f iikm angles ^enm in tbe ©keteh • 



S9 



ms 11^^%,% trnm^ms tmm ta ^als sleets is mm 
^e %f Ig^ ^ m(^e«aiBat& fmm 'd^B&eib^ pee'tt^mOy* Warn «Q£d.e8 



@ i^ p can l3@ ij^ititffia l^i^m ia» gecMnslaQr i^ figure 2| 



Slies0 y»3.fttil-qiit& csen Iwk iMaabSnod. iio yield 

8ii» 9 « sin 9q 8iik(i 4> ^) 



6la ^ - (S^{^ « - [«^^«0 - ^Sj (^3) 



eos I 



fet)r^ ♦ oot 9[sii^«o - sii^s] J (1^) 



Ii|U&tl<»m (iXh (^)i 3^ ('l-^) «X|ires6 all the -variat^lee izi e^uatdoa (10) 
in tema of t£M» varia^bilss of iatetgratioai 9 asd 7> 



* 50 « 



Wm itum&fBUm fm f m9~ ^ dcorled out ljaD0dl«it«ay» leaving ozOy 
tlie iiititgrttUim idtli x«8ieet to t to t» peevtMA* ^m reftulting 

«i3^px«.sel4»a SMir '^ ^i!ii3«d iJitQ eimxi and oM tcae^%ixm& of B@> or 

• 5[sia %]l^(%)> ♦ <^% |32[eo©5t|e sin ne]»%6C0o) 

♦ Sk^ \, 8i»\5]l^j(&0) « X€[oo8 tj^ «la \]%(V) 






t^ this tibteftis tbeify liaiw bt^ inisaericalJly izitegrated asod are given cm 
%0C%) • l^(%) » / {eos ^ cos 0^ sio «de 



/ ^Talu ft sin «"^ siu 8d0 







-32- 









W0 



f'^(%) • / -{jEwis uor^t^sla M0 










r% 



I {sill «)B% sia a"} sin ed0 



J^J5(%) " / \8in ^ 0in 0j> sin 9d0 

* V 



I^(%) « / {cos 9 008*0 _} sin 9d0 



55- 






%${%) » / {tin ? «a^9 iiia 6y sin 0d0 



it^ 



* 2 cos 0©) ? ♦ ^5 < J [eoa5%j (i • eo8^%} 

♦ 5^[i8lii^t|eJ(® "^ 3 siB^o eo8 ^ - i» c»s 00 s1b^0o - 8 cos %) 



m J4 » 



mA ii&mt^ 



% 


» 60 • 


eg* 


% 


% 


» Cj^ • 


3*^ 




€2 


» leg - 


- 8«% 




% 


« ^©5 






% 


e S<% 







^oA 



iinra^e'tM ipi^ c^s^ es^i^td 0ite» ft^ 3ml#timt g^siK^i:^ is atom in 



2 



fte M^e 90 w€^ ^itos^pt ma 61^^ imw^ tii^ proper visXuaB of tli© 



- 55 - 

w^ m Qm^^ 1^ 9 0,02®. Fgj^ » o.see li^ « 0.106 
fg^ • 0.039^ %> • 0.1*90 fj^ = 0.^ 1^5 » 0,:^ 

f^ » Q.^TS %0 * 0#5TO f3|0 » 0.1^ f^ » 0,202 

"^mi iSmm mMmm sm iBtrotaeasa iato t^ deHt^Lag «^pati€» for Q^, C^ 
<^Qd 0^ it is j^»asA Itet 

% » 0.(^9T sin t^ * 0.0^3 sis n^ ecws n© - 0.0^5 sis % ©o^^ 

% * ©.at * 0.^9 «!0S % ♦ 0.^5 m9^% " 0.195 aiu^ng cosing 
•0.12K) «>s^Tj|g - O.OiTO siK^t|g 

Gj « 0»:SSS^ ♦ O.Jt^ «go« % ♦ 0»2©65 a>i^% • 0.1993 eos^% b1s^% 
-e.l5lfe cds\| • 0.0081 sitting 

&9 c^ose m &e m m m t ^miismea Qg «Qd CN^ is striiclQg,id3ile % is 
asall §M. «a oM ftuustltm of \* ISa&m soluticms are slotted o& 

It is eetsily %Q3iBii>Bt«Ki& that ae dg inraroases tite ele^ee agre^^emt 
bstmran d^ axsl fih^ inereases. fbia for the 9^ valtae tised tore, 
0r S&t larptr inBkluea tlie s€m>«rUM "she^ fsetonT for earth tlier&al 
end albedo I:^atiag 8¥tt loeea^y ^^ i^om provided tite intensil^ of t^ 
all»ao (Ja) is iieasm $^»»i th* 0&tellite*8 appoint aiad lorovidea tbe 
SFpneterttft ^^botts net se* pest tbe ^terl^'s texsii»ator. 



11(011 efial^^ Cl^) ^^ ^^^^ ^ oiamOate 1^ airtli^s t:^i:Bal pmrni^^ 

^mi^ tmm 37^ M^ ^ ^m m^^ efm^tcad^ re^^^^j. t^ k&sP E et 1^ 
eartto*! fcAar imgl»iji it is A#» tim% 3^ emad ewUy ^^ \^ m 
«i^ a3 ^ pari^tnt of it0 BmxiiMsa vilt;i^. It mmld 'be diJXieult to 
obtaiiia -mty a^enr^e remilts wlt& Bxmh a& Mtt^l^cmi h^i^'^r^i tlie 
m^ aite^iaatli^ is tc» e^iatruet ^^me t^^pe of J^ map {£^t tim eaarfch) » 
Utoforteiimteiy l^iare art «ew If aiosf of ttose in 0:gl0teiiet^ F<» Wb 

itear ^l0 ciisist te^t %« a6i^ie|ft>i^e siaoe a i^smlimtlcm of ^m B^Am 
after ©etg 4^ -iijil isCaMbai^ ooi^ ^^mt a 4-feyc^st eri?©!* ©-ver the 
ssa^^iate j^ 9, Hat platSj^ wMeh Is (in @, mme) mx 



©OS ^ iia plcrlflsed te flgtcee ^(a) . & tl,gure ^(b) 1t»e sreswltiag 
@^(^) ina^uesit DcKT l^^ta ^b^rm tte earth's surface of Q m& 3^ 
mix^ma, MlXeSy ar© piotfceA. Sbte -Kalues of %C%)/C'^)3g,ggg, e^^uated 
for OQ. intioite l^eig^t ^bove ttse «®rai's siarfae©, utisre iJiCti) has bees 
texidas^e^ sf*(»? oe>s ^, is gilsitted la flgiire ao(s) . flie corz^spoMiK^ 
esiaet ^dutilUm fiear 6^(^)/(^)jg^ is plotted in :d.gwe ^(b) . It shssjuld 
^ iipte€ feef« titsfe %(%) gl-we® % Dor a bod^r of my sha^ if loaltiile 



- 37* 

It^t TOfle^^tlms mm rngSJ^^Xm laoA if -^^ tn^ ^wb ^Stmst aorae axis 
M.^ m^ii($i^f^ i^mA m ^mt w^ amtl ^^i^gigeis in ta^?ei»tuiie oeeur 
^Hfij^ ^is^ u^i^ifGL^^ii ^ftrip^ip^o^* 0^tei*wiae> '^te l^o^ ^^li^ipo w3m% eomtcfsm^ 

of % -Mill le ^t@!®i@a la.t«y. 

1^ ^aetilsM^ &i % i@ Itefeiiiinit ^^^ 1^ sn^ fetors t^cnm £& 



t^paMo© (15) . tn «^ ^«i«^peat of »a it tias assisaed «mt «» «Kr* 

faee of thB ewtb "»& a tradUPoai &ltf^mt^f&^ reflecting s^iere, Bie 
la ^Atfet 'tite 0@r|ii, ®jia its afeips^e^, s^^fefeea* maii. xaefiect eimllgit is 
cptl^ etsffipl^sti lagaewr, it is .em^steft in j?e*ere»^ 7 tJiat ttoe easrtai*© 
albea© Kii^t twy l®twg«i j^ |«pa®nt sat 58 percent, A l^ge p«ryxm 
of «te al^<l» is te8 te ea^wi ©a-^r '<^dL€li ai^ sr i^ aet toe tmi^s^raajr 
^slrita%s»t ii^@i^ m^ mspm*M mpfem* mm it is eymm^ medt msm is 
mm f^xttlitgr in ttttetai^tisg m mmst solutiem t&t \* mtb this diffi- 
0ultif in sdM it i^ppNnro tSuat tbe eeriee ^fsrassiaiaticm for tj(n}^ fox* 

Ste SiilatlalUoa of %# uaing eijoatioa (1^)^ also has 1^ adima* 

tags of tiitq;4l«itr oad waraa^tilitor titiet vas iemn^ in 1^ calculatioa of 
f^ 19^ ^0 soBie p-deeaib. ^Bsmv ia oaoe t>ig feiliisg atta«^d to efaa» 
ti(» (l?) sAmoi in ite ae-mX«pasiit tlie aeaun^ticm vm mxie that cos Pb 

i3m mx^*B tttntdstaitdir} li«x*e f»a ^g is s^ro on the tendnatcn' aoi tbe 
portioOi ti£ tht «iriai*8 marfoee i^oh is sbieiaed fictm the aun has a »egft- 
^ve 'Vttlw fm <M« ^at Siom those iaagati-«e valuers were 2K>t deleted 
JSOBi tlws iBtegratiiaQjr 0^ a» (teseribed Igr equation (15), is in error. 



fifce jre<ils# Btim of tMn error <^i^ oiflly be ieib^rmlxiaa h^ mx m;jax:t 
a^uttc^ ts* atpi^lw. (9) * Ito^ii^^r^ It 10 clear that -^^n e^iatrfLc^ (15) 

# 

latter a^aul-to la mints ^ #^ 3^Ba t3ten tte 0»t^ #^ a<auticai^4 
M MBM m^t^^^^s^ tlie <^d part of % 1^ asaXl o«®^are4 to 1430 
€i?exi p^rti use of ttoe ^aM ^^(r% regirfjms tl^ d0termlTi^l<m of fQ iifeleh 
is iM> st^l# n^iijttr* If ti3j0 oM part <^ % Is mgleet^, and only 
m^ ^'mu pirt ^j3^t^ flpire l^Cal sfeows ^6mt d^ ia elighlOy larger ta»i 
ttot n-smi part of t^^^* l&uu if C^ t© ii^^A iia ^am of Sg ^re ia e 
c^^l>^i^isti^ e^^et 3ter -e^^ earrw ladt^t^^rsa fe;^ tw^Ming mgatlw to1w0 
of CO0 P0 t:^ ^te tii.c^ati<m ^f #^* 

^ thta# rt»^£i0 %(%^%J ia n^A la place of ^Cn^^Qo) to 
tMs t^0ia. «tete^ ^bma.€ also tmm^^v ttiat S^C^^S©) ii^ ai^fe si^l#r 
tc» ^3u^ ia 1^ «ml3rtietfl B^mmB. 

i. ^aeyJji.tiffi €^ O^^tmtiqix te^a 
fbt ff^eetli^ dt^^^^l^^^i^^te ^mk be ism^A to ealeulate Ite radiant 
^^iS^^ nn a i^pa0ea:^iit^® ^^^^iml iiptrfi^ a^ a fi^eticm of 13m 



%» %^ %^ %^ ^^ ^0 



** 39 * 



<^Bter» 1^ fljpyri^ 7ii tl^ ^ iPtia eoineiS^B id.tli ^3m eartb*a north pole 
l a^yi^ t3i0 It axis is |^£^ir]p^iiii<!^3ji3f %o tl^ #art^siiB Xin^ nt Ite Eim^r 

i^out tht Xx i^^> ^m3^3#i tlie iiigl0 1^ until tl^ ? a^a lie© 1b 

Wimi^Xsr ^ r^tstimi «ftK3iit ^Im Eg axis^ Mirouf^ ^:^ aisgle 1 i0 pro^ 
viii^d^ 00 tibat ttst K ails j^mmB "^s^m^x iiie sat^lite iti^ W^ 
iXfl^%) ttmm c^Bciiea iri1& tbe (|CSlf%%*) £r«Bt* flie c^K)^:*diiiat@^3 of 
aapsr poii^ fC^St^E*) li^ 1:^ ^aleiilatad £r€m F(X^¥^E) l^ ^:^ 



X* 



< t')- Q(i)Q(i)a(f^i»)< t > 



%' 

^ ^ 




^0 0fil ^^ ^^ ^ 

"^^ad^ 0^ c^B 0JIK 
IJ 



^(X) 



10 

@ ^utn I OO0 X 



Il 3 f^ 



- if© • 



^1)» 



mu E win £ 

L © ij 



0^ ^^rTTyfii^ oirt "8i© f i i# . l ^^§te^. iiddltdlp3.i00.%ii}i;i 



Q(1)QCI)Q(#«|) - Q 



is a ma^ariK 



eH^m^ts 93:^ 



^ » eo3.£ co@ 0^ « sJUa S cos X sin 0^ 

%g » *«t& S sin {ljgs( «• coe B <»»« I eos fl(j|| 
%^ • sia X sin 0JP 



^3.eo»X 



[] 



stttsare matrix iMa.e{^^ denotes a eoltism 



fo locate tiMi position of -te mm ^elati-ve to tiae eaartb start 
aeedn vitb the earth oentered {X,t,z) coordinate frame. (See fig. 6.) 



* 41 - 



first Wm mm^ msm rotated aS^Mt 1^ ¥ axLB^ tbroiigh ai^e i tmtlX 
tto X mis pot^^ t^ tto mm bA tto si^i^r 0aX6ti^» Ita this poaltloia 

foiiita t0 tiie ami m^ the (X^X^E) £riiTO ^olncd^a idth l^te (X*'^Y*%E*') 



r 
r 






> « %C8)(^iK 






^&wre 



^a) 



@ 1 



iM^lA 



tCi) 



ecMS t © sin f 

10 



Q(fl)a(i> 



"^ Si CND0 i sin eo0 S sto l" 
«^lii ma i €^s 3 «»©iiai 3 sin i 
o^tla i @ «mB 1 









tSaCOB 












^m:^ %m ** 






©o® % «« I (**t4B ^ ^m ^ * <^© ^ CS00 I Sim ^)(€^t 8 COS i)J 

4^ [C^s^ >@ i^ii I)C^^ S Sim l)j (17) 

*f [(eos E tin 0jy|| ^ al^ 1 a&i I ecit ^^)C^i^ ^)J 

# [(sin 1 ate £)(€»^ 8 ate 1)J (l8) 

X s^ ?^ ♦ 1 Ml 1 «« 5 4^ X 

f m^ % m^ bt eatl^ii3La1^ from i:iff#i^i^^ S» ^ la ^to angolar 
Sli^pOUMMSEk^nl o^ t^ 0ii2rt^ idt>i^% 1^ iPffij^ nit^ £^ ^8 ^.^i , to S0TO whan 
At ia 1^1^ « i if tipt spm^ermft^a aHigyXar position Ib orbit ^g^mi^d 

f!te ^^#Btati€m f^^tiMe# a3j^a^ <^au3.at0d in iMa section a^ 



^^m^iSjm^B) tsm^B wm"^ ^ its m^^mmM^mil mtUlit^ l^tc^mzse it (thtg^ 
^^4^^ ^^p^s^n^e f:^ii9^) iii i^t tis^ In imrtial ^p^)@e# l^om 

After ^^^pljia^ Wm ^mfiMtlmm fm^ ^^ %^ ai^ M^ t^ al>cn^ e^^pn^a^c^s 

«^ % « *»^sfs V w$m{^ ^ t) (19) 



mB Bg « 00a € 0oa(s * 5) (a) 



% m^0M ^%'m^ mxk^B j^^o^eeticm <h^I^ c^it ^mm mA j^ri^s^ 

e:mf% p^i^i^ ^i^^gPi^ ^itrigae 

tar^ line) ^Uy^ ^^^ tte (mm effiiAi Xisii^smt^311t^ ^ar1& lin^) plani^ 

%B ^£to£1Lii^d> toy 






cos 70 « ♦ ,^,£,„fyAl^ „lt..«S^„,f <^a f .<?ffg(^ ,t y),e^|6, r U , ,■,,,„,., 

(22) 
ayri^ (3) ^t OidlCMlE^^Hl. 



^ k6 ^ 
F* Spe<!4l^iimti<:m 0f tb@ ieat Eq[imtlon to 

^kmMMt ^ apu^eriift in a j^ar^^a^tiib orMt raoelvlBg direct i^^^lar 

^^ftoen Bi^ CNS^ii^ai^ c^ 0li|pl|r joii^d cin^^Bi ^lii^i^s^ and Hat 

It altot^d te rmim^md tliat f^ m^ g^|»iau:^era£t it i@ inprmetieal 
t^ i^0i3^te mm^ B^lv^tmm fmt ^i^mWm {1)* Ss^^ vimn aa awra^p 
taapgifm^o^ mm a ^^ri^imit of ^^ b]^/^&^^ ia miffleieiirt^ e^pmticm (t) 
mlibt te ©^1^^ "^ffa^ im;dti 3^0a <^^ipx^^ag^ a£foH» S^piatioii (S) ia 

Ixm iSm m^serift 1 temi^^ Wm steMi^ foi^ iMeb ^0 efimtiim is 
^gritfe^tf % is ^m ^m% flii:^ i^^arl^ed ^^to tte ii& a^rfac^i a^ F^ 
is tii^ fo^t^r @ei^r^ta4 Ijrt^^^i^^di^ m^ ^p|a.i#i to ite i1& ^oti<m» If 
mmiB mWmx metlm. J <i^ ^€( ^pam<^ra£% ^^i^iets ^at ^ t^ ith section 



*J,i * ^4*i(5?A^ * ^A^) 









Item #fyi^^fdUm {U} la ^lU^ #i:^^q^[at it ii 
S H 

^^le^eip^ spfijtdrai l# not 0i^£l0wrtly altered t^ tfe@ aarth'© aeattesfti^ 

%i ^ % 
Itois i^lcma fircia t^ fa^t ^^* im^t spaciteimft we ai^^ mar to islie 



It @]to\ili. b@ m^& that ta e^mtica^ {^} 

^ @&e Hds dilT@t@iiu3e let 



f » f^ # V 






^^ " 4 / {^^ * ^^^^"^ * ^%^ ♦ ^A^^ ^ ♦ ^**}^ (^a) 



\eaXfSk titles tliat 

If ^i 10 wteb l^f0© tliaaa fA^ Idtoi tli0 l^t ^vw. in ^^^mtiom (25a) 



• ii-9 » 









/ (^tfii\ » ^Aj%i^ 



^^tll0JPl> 



ti^ - :: %^ ♦ ^i^%t® « ti^^ <i ♦ 6^j > C^) 



@0 t3y ^li@ MmmieU e^MsaoMon tig&@r<a% 



ttd D^tetlug M^^r c^riisiis^ t@2;s)iSj s^ msl'vlag tOF f/^» tinea 



% 2 "^1^ - i(^ 2% (25) 



Xf (ViM)^ in «n <»»^ar«id to o»e then 



%^ » 5?A^^ (25a) 









11 



Bj^m&^B£% tupii^ mm mi^ about W» sasls €€ i^anetxy usruaU^ 

mm &m^ ^smleA msUom s^f me ^paee<»r»it's &imtm& mat lbe di^ded 

Mt& mski2MT em^Mmm wMX "Use «wt^%M*m 

m mmis^0 of @. ^«^»tr®ft ^^t^ tsmSmma t& the i^isai^iry^^iaB m^^s^^ 
in aarxlviiie 6tt o^pMktloa is£} aiid een be ueed as an exm^e to lljLustmte 
Ite tise of Ite sgrtteift ^ «^piUdas aesortl»ed by etpatloa (26) . 

into IS eeetlicms. Jto ttfua^l^n fme eax^ section is vritten aod bXX 
3JS e^pusMoM aare latogmted simltsaecnuay^ for sei»x>ia. orbital emai±U,<xD^, 
tmt s«p&8«e OCT timiaX a^fiisitton;, » i^tetusre of Isq^orer XVI is presented 
as Itgoira tiCft) * 3^ flgux« 21(b) Escgplorer XVX is ^hown idth each titer- 
Ml @eet^0n im^fed« me ^te»al inret^rtiee l%»r tliese sections are 
listed belmi! 

seeticHd X itcmm:^ soler eella) 

(fflC)l m 0.1^5 Bt»/% 
Cil)j, * 32.2 In.® 






'1 
(Z|j^ w 0*09 

fl»iwdL s«cfct«Has 5 |#ii® asO^" eeHs aial ri»g) 

(ae)^ » 0*97 
it}^ - 0.79 

(%)i^ » 0»71 



• 52 •• 
mmnmX meUm 5 (telaoeter uKxSales) 

(me)^ « 0.356 Btai/*^ 

{m)$ » 1.6aS Bttt/% 

SKMmiX eeetjUm 8 i$mme ^st shield) 

imi)Q « 2.00 Btu/'R 

{%)^ « 0,19 
(£)q ■» 0*16 

CjBe)3^ « 1*677 Bttt/°5B 
(%Q « 0.8a 



' 53 - 
Si^j!iml sectioa 11 (€k^&ard sensors) 

C^n « 5^ la*® 

(A3j^ » ^ In*® 

»9,8 "" 5*63 X 10*"'^ Stai^B • ^ 
%,4 » 0.06 X yf^^ BtaMa * *^^ 

3!l)e 4seia»itacrtive Iwfsad^traaef^ ooefflclc^its of is^ortaace ere 
1%,! « 5»1^ X ICT* Itu^^itSL • ^'E 



m ^ m 

hi.^2 « 0.10© Bfea,/wla • % 

%,!© *• ®"3.5i!M5 Stet/fflla • % 
%0,11 " 0*<a87 Sttt/iai» • % 

!i^^0 « 6.®2 X 10"^ BtoMa • **8 

Jtar ^ffipi pa9N»M8 wad lie^peratta:^ ealeulation it hiut Imen 
aesusaed l^tefe 1^ tiolQdmtal piD«er dls6i|Mgt.t«4 1^0 0*% ^mtt in seetioo ^. 

n« iffiO^ of Ite ecaiiar eonsticit)^ used ia «be e«l<mI&Uo»i» «a@ 
©*02»9^ Btii/^»® ' «^> tte ea}»e^ (r^) tj^ed HiftS 0.^* She if«ditjs of 

Ite ««z«ti is oaajoaetd t& be i^^paroidLBiEGlely 3M»X ikfiutieai. ffiCLes^ and the 
»@»aiml ox^bit )m&. m. mmmt pert^e of ^It^ wmWmH laiXes axHl an 
apogee of 4x89 uaixliocaL laiXes. 

siiBiatitnecmiar t<s^ i^ ^ s«otlon6,-aM for lOse orbital ecmditlons 



• 55- 



mm&U em la^tteA i» mmmn 18(a), a.8(l»), a8(e), X6Cd), l8(e), aad 
18(f)* 

It @k»il& l!@ lao^i %£^ in tb@ee j^lgiizee mi& Iste^aticm Ms sot 

#^pili)»£lQm mlix@@* ir tte intapr^ldUms i«gx^ eoattoied HMefiMt&Xy, 
W» imX&)B^^^ ^^^@r|%%air@ vpuld t^^od. td %^ F in tl^ coldest case^ sosd. 
U^** f ia t&® fastleat mm. 

B^&mt Ml wm mw&M&mt^ Imm^mS, fx^& Waller Islaasd Sta^^ 
m Beceaber 17* 19^1 m mt mi& i«rltlag t2»e ©pa^eoraft is etiU treaas- 

mms Ispjrtast @©cti»»s of ^^plorer XW[j ©ss flettecl ©n ft^ires 19i$i)i 
Wi^h 19Uh I9i^h ^9(«)i i^ I9{fh 03.90 12ie aesdsssi mi sdMms& 
tfimgi^«ktw«»s p:if>ii&lfta f^om fiisme&u 2B{&), lB{h), iBU), l8(d), ld{e), 
mA lB(f) aa^ s&oan i&m r«f* B aiso}« 



6. A VmmmHaAo StudE^r of Orbital Beating 
A p«r«aietrie «<»% <if msm^'m isS) i& easily tSie mat ipamttvl 

-tool a-mllflftild to tlw m>eH@eisr«rt ^^a tey ma?. desigmr. 

If ema ©ectioo of a Bpacecr«s:ft is tree of iflieijaal cxwqpling viVa. 

otiisr 0eetlo«8 of Hie insMfilei ^mi itfi to«t b6laz»» is greatly sl^li- 

fU4. m& iStm mmt fMadeeuaBt^ cliaraiCtexiBtioe of equation (£6) appear. 

I*c»e> <»eEWfa.®i efoaticHa (^5) becomes 



m^ mHiet Sf^^p^^Uig tilt 0tit^0a^ipt t* l^rom tliie i^r^idd^os teveXopB^nt of 
1^ aad 1^1^ it Is eltai* ^tus^ ^^^ €^^^m$MB a term i^^ la mH^jgOSed 

Vmm'mw^ t&l& ti^rm is mis^ m^ its ai^r^ge ovi^r ]^ ia Btiro« fco^ 
f^'^m tigmm thim) it is evident tbat 

fbia ii^t iip^iadiiaticm idLH. 1^ um& in tbia sacticm si^ %(%^%) 
ia wicli mort iwii^i«t»i€ to miml^^^aX treataasit i^mti 6g(@Qi%)» M 
«,r«l«»., m «« «ltgM«4«g f^ Of i.(,.,9o) c« be arrived 
trm&. tbe ^E^Oloidi^ aoi^itemticma « f^rcm efuati^i (9) 



*te « f ^ J^n)iia 9d0d7 



i^«a^e 1^ 0i^^e0 *y»i^ ^m spaMC^eraft ia in ^to *'laig^teim Bpln 
«*a»/' i&^r t&e i^0i;^^L^^ u@e4 to dteriw SCn) it oa^ be sk>vii 

a(n.f)«a(f.n) 

ani If (n * «/S| is repaaneed by a, tbea 

S(a) s il(-a) (29) 






r 



^ r«r 












so 4^^ can h» e3(pE<«ssed sa 



{[a-<a>|*<a> 



^0 «fi 



C^ 



&J^ / / I fc -. (0)1 4- (a)>slii 9d§d>' 



€3^ 



#^ » 2J@ a(0X3' - ^® %) ^ ( ~^) / J < [5 - <5)J > sin 94Say 

o ■ 

iyrt$r m^%^MM^ Wmt Xmt §m^ ijit^^aX^ l^ten 

% 2S aM^Cl - COS %Kh) 

mm^ (A|^ t^ii» 

i^ s (ly^ci ^ ^^ %) (30) 

* |C&fe^)(l - <»<^^ %) * ^ft£««A^ (31) 



* 59 * 



[ii * <S>] 



a t 



^ ^b^ l£i1^@r«l Jmit mgl0^^^« £^ IMS MM^ 



bter^ii^ tu % 



5^ 



■^a^ n^/g 






M@ ^t 



a^g A I ^s 



$§ m Q m l^m % i» || Itet i#> i^qi^^ll^t (j^) is emet for ei^i^r 

ihe ^^^nl^iiii^Ei 0f ^0 1^ 'i^a %e^^ly3i<i» mim^js^u mo pric>r 
Ic^i^ii^i c^ i^ @ri^^@tetic»ii 0f tl^ i^Ni^€^^<:^ig^« 

iter« T %M ^^U. tUL^^N^s and p ia i^ ^l^siV erf «^ sbaULji 



"•l^-^^K^) 



1^ "f ^0 B^ 



(% * eoNS 9^ 



OOtS € <^>S^(d * 5) 



Kw^*)(Ll»L!2) . t^jk 



(38) 



hssMm m.'^a (f^ ^ «3.'be#ei m& mm^ iSmxml esergr i&^iSmxt tm 

iMim^Sm&e^ iJ&te ^^g^lsim (Jit) W mnHJB^rim #qpatJU«B (5&) « For tMs 
«to e£iS0ts 0t m%l% aeem^rieltr ^iii^U^ ^ se^tsetM ia this 



^ g^ 4. 2^^^ « tCt) (53) 






-^-IWt /^mA p'^^ 



J ^«(§^)*fe - (*«*«5 / «»A « (•'PC>[*aC* ♦ 2^) - ^a(*>] 



% Ib |ieflosdl«i tm 1*0 tills integral vaai^^s. Bow set 



%"" • it It ^^*^** 



* 6l * 



''{^]*iMim* '"^v^'' 



♦ V%7Ci * ^t %) {^) 






T-" 



S:j ts 0,65 



ss 



I 









^ypL« t^ [Least 'iil.tit in 

%^ « ^7 X 1# or f i^ 2 32^ F 

aM i^l»s^ liiNtti^ loiters 1^ ^^^i^iytt*3 t^s^peral^srei him^-mst, ^m 



(^) 



\Z J 



m&lmW^m &mixmmmt is at m l^^^e distance £3t<m -i^m iji^mtimm 



tp»» tlie smMmm imm is aot aaaU asd tonee is not 



toe ^ ♦ Soffy^^^ « 4(t) ♦ ?i(t) (35) 



f{%) (mm wsMfiM^ <|(t)) iHiadSttrea «b0 enror ia ueiag f^ » 3V ^ 



^%;i ^ ^^'(> «a&e« is a f^oaeticm of tiae. AXao^ 7^ <»uX4 be 
m 

«A » (% ♦ 'so)* 1?0 « ?% 



m O*^ m 



imw^ 



fA* 



f ^^ ♦ %0% ♦ ^Aq^Q^ ♦ ^Aq ^ ♦ V 



(36) 



Wm& &^^%imB (3?) fiE»t (3^) as« omSsiseA uli^ efoi^ciii (J^)# tiie 
t«M3.t Is fonna to |}@ 



tlDt© 



5^ ♦ *'^' 



* Ser 



%^ * ^%^0 ♦ %^W ♦ ^i^ -^ ♦ ^* 



* m^ W.00 ""^jt ^ '^^iWi * '^1*'^^ 



^^i!& @tSG|^^$^e@ f^ 



tae 



&t 



♦ i:«r 



^%H ♦ ^Aq%^ ♦ **% %^ ♦ n)** 



•fi<*> <57) 



^A^**?* » ^%^^ ^ ^?/^ ^ » ^ 



Msm m%Mx^ 



fi(t) - ri<t) ♦ TgCt) 



tibea if tlilfi ^pljolism le sti^fitltKited into e<saatlGaa (57) > and tlie 
melli^ nottHmar inmm are separated into ao e<iaati<m t&r v^, tl» 
Mi^t 10 gl-veit li^ 



* 65 * 



Tpe ^ * ^[^%\.] = -%Ct) 



m 



§^^& I^In^ Blljp^&^l^iiElS ]^ PB rt %M 



4% 



S/m. S 



ai 



Tpe _ ♦ Sf ^tj^-9^ ♦ ^^%'Sj^^ *m^yi* n^) 



*■ {mmXXm' wmeMamm 1^«b«) » *r'g(t) 



C5^) 



^ « % ♦ irgi f ^ » vg 
% » Fg(t) ♦ %Ct) 

"(Mii «ysa»tti€m m^r ^ 8il!>0ti^lsctd into ^fuation (59) fiMj ^opsn 






^%^%* ^^^%' 



-rg(t) 



(1*0) 






% - V^*^a*5?iij^i*^iW2'-'-%^ 















l^mBtUf Vm pn^per fii^n^ «if r^^ is 

if Tj^Ct]^ ie 8«3.«et«& liisr ««HikUo» (5!»« «b& if f^ is a 'near 
iOlKUim* t0 7a« SIsus & 0«a.utle8i le ^tetsijaed as 

^^ " ® { ^^% h ^ *" Z^ ^^^^^ ^ noting forijliig ftoetl^ 

ISm ^iri^0pi@^t af a acawyi^sm for efiiati^^ (315) l^^i^^ to IMb jpot^^ 
%H^Mi^ a^ ij^^^aAM^ w^0x^s^^ inli^i^ii^ to p^rstiis^ ^^te i^eiAti' l^b^ 0013^ 
ii^ ii&^;yijm m^WmA ^igim^* A0ti:^aJL^# ti^ir^ i# a im^ ^^i^^ »t^a4 0f 






•^ %J 



t}*^ 






{r^>»®(fAj 



In eiwqr tttlw rL|» Is tta^t pewrtioaa of f„ vhieb would cause Sa 

$lt«( t»Nscii^ Bti9 {in l%»3i»e tiie 8e4ti«lQiQ to m* {^3)) is to mMs* 
tt^tixlwi tb« aamsaed ^^iiUcm f^emat into e^aatlcaat (35) «»a reqitiis!^ HwA 
t&tt Sf^ftul-yUe 4%Kpe««eic»i be satUfied at eaeb order o^ negnltude Idvel. 



l^^^af%^# iB ^lia tteMs^ a ^UUm^t ^fprtm^ will b0 ns^i 



w • \vl * vary \^r/ * '" 

lSm»t mSma t^s i« @iili»etltutid Into efoatlcm (55) it Is ^cAmd that 

(1^1) 



fim& a p^mtimm ^i^cip^^t it is eldest i&m% 

m^ fmm 1^ j^mi^mv mmXjc)f^m^^ it i0 sXbo ^i^ims list li^^ 
<^i%^ iKiDy^As fj^ is m^t'^^i^* It is also e^^idiest t^om. ^pa^ 
^L^^ IjS) ^te^ ^ite iiDiS^t p^if0tieal <d^c^ of f^ ia 

f^ itt «iy5ta3at| -— ^ » {^2} 

li^pii!>iaig iM^ li» rwnufnlug tenas l>e satisfied <»a s^^psonant ordber of 






f0e — & 4> IKi^f ^%/sg s. -r06i3fftQ%Ax^ 



at % ^ \. 



axi^ so tmVi' 



- TO * 
lit) » -"^^^ 



(tp«J«*-i; H^ i^iMt/i^}t/^ « Car) 



%t^ - %^ « ^%' 



'^f. 



V% 



* 1 



<^) 



tin) iilA<^ i0 @#:^ to C%j./^iw)^* after risni£itii%» tise eioi^cfii for 



(tp<s?gA0)g5; ♦ ^(£efiy0^)t3. « (2^Ao^) leo^ - 1 



ifjl 



{^^) 



Mem- mr^M 



Q 



Ite iffiOJUkEMiiiii solx^oci of eftrntioc (^^) is, £rci» r9£e}rea»c^ 2, 



h • ffl«a!^(«>5i t) jf «K|K>f ti)[le^*^- l]4ti ♦ cj. ®i3?(''>g; t) 



<£te onl? {tradition iiiljaeed «« tills result ie iSm^ i^i^} » |]^(t <{•£>, 



* 71 * 



hi 



rt 






so 1@[|IL% 



Ij^ *^ ^3^ #ig^(*% tX / «38^C?^ %)[t«t^ * 1]^% 



i^ 4> *H«M|H»ff 



-% £) r^ 



X «• i^l^i 



1% 4 '^'^ *^^ 



k 



• 1 



d%, 



(^) 



Si« <liffM»iaAla3. @fi3a-y^t for 7/^ ^^^ ^ reiolt^ai as 



(tjKSf^)^ ♦ MS®fA0^)lg « *6(£«fl;A^^)ei^ 



Zts iK&«itie» is 



r* 



tg . * I Jigi ms^i^hi t) < J «aj|»(>$ ti)[li^]dla. 



•a^C*^ li) 



ia^i*Ai^ lb; pit r <»i I 



(»*7) 



Ab oidtt^ of t/i{t) e»«R ^ eluyim as tcOJuens: Vm average -^railiae 
of ^B foreinf jtatetion (rifilit*li8ffii3 side of eg,. (^^}) is s«7o« besce 

liSiB iae«a n^ue of 1^ is mvtf, Bomvmr, 1^^ «aas l>e vrittea as 



. 72 - 



h^ « I J^ Sx%% ♦ fi^ - 1 J^ h^^ij 






(Mto all f^^Mi^ii) of m wmm valiiad tiim pli;^ a term nM^ 



^1 ^ *1^ ^^^(*^ "^z / 



C-i 



€i^\jh^ %^^% 






• T3 * 

i^r a fi-f^ wmm hm^ tm^ fi»r carbltsd. :^ass@» @aA £^ ?i^ e«i»X 
til mwo, i^mm is a aisrs>e&pe»3aii^ m^em. -i^sapesutisre Sf/^ (ae e<aleiii» 
Xmi^ W n.* i3^)>* A@ % pt^m to «3ffie f^site mOm, Ix also 

aM ^^ f^ m&rmmm in ^reeomd^ «ii^ emmm^m C^), Xt is 

#f tit ©issi €€■ 



.'-] 



It vi3Ll te i«m$-lam%&4 la«@£> liew tli^i^ two facts eeee of ^tiA 
is tue |N36aite ^uexml SsBiga of a i^&mcm^* 

in efosctlQii C^) i^eii dietiaguislies l3eti»e@Qi -woirioue 
}| 10 1^ psmm^v (>f)* ^ iospectiosi &t eipatioo (^7) 
13ii^ ti«» eixem€Umi» vSsit^ coofttaim tlie rxMalimar lunspertids 
M» tffiap»p«il %a3i|i«r«lwn» f3,metxiaU«ai« is also defiaad \>y {>$) * 
tte tteqpieriil tiaa#er6ti»ra Huctaiatiosis are a ftmcticast of {>^) 
fur a ii-«e» l^g^* fliie p»:g»v^ ca«aXd also be deri-ved from the 



It iteuM l>$ x«iMtl3«d timt &et^ is the ratio of surface 
hmA mH ii»dA«iit aa Vtm e^^acecraft to tbe surfaee eoid 

(>$) i« am^tmeth ^ mit ratio o^ tiie tine and spam averaged l»at 
imta isal^i^it on tlie spa«»eran to the aean hieat atored io thesb aixr* 
tern* fba fa«@tor of 09ao tparttsr has no social signilic«aiee for ^lia 

partiStilAii!' intcs^pMtatifissk of C^i * 



.7%. 



l^osf i@ giw» &t33e@ It is ^mi>«»i2. ^ta^ mie exists. tmUa&g it idll 



a8l,ttM<iti %imS tei^ ir)iAie§# t# '^ss £^ten fused lixjearlsst^*^ 
1% ll^s 1*» 3«ia# 0t & ©SBStiBSt. fear aa ^amaifiM of 



tmvasWi- « «i««itt3. east of i&m f^oOloiiiag seeti€@^ 



mi& mm ^ap&am^ fent^ai^]S« M@<la^U»itio&s 

}*& m^mcmiX moftm^n, the solutlda ot the „&^tm. oi 
m,iSmmsiiSjia. msae^Mm {@m^sfiim& t^ eq» (25)) asr ^ exeeeslwly 

twt 4l.itt3dP>^lt$Q9is fq^fl |)ti> ftemnd in tins solution of 

£b feMz«3lj B ie 8s«aro wi3ufi»B ele«trle eurr«!i3ita flov Is tte amilmri 
tims f is of oo iuteffst hem* fh© tewa ^ is the araaiaafc £i6at 



Htm (anlvt^ m& li^vlng) tbe i?i^da4lar shell surface* flie g^ 
i^^^ Is ^iss teat ^rmmt^m^^A^ in tte whicle*a taii®aiat ^wim, t^ 



difXieiat ^m^B. 

ciualigiag tea* «At0- ^iiwa m^rffe^a reoel-ve sas^^ teat thjm o^Wtera, 
%l|j^ri«l ^oHm mmMm^B mm mm imbmml iw^semimte ^Bt» for IMm 



m mSMH^^ ws^m m^mm'^m im^ fig* 10) x^t 1^ prfLmrfLpal 

is xi<sx|wtidi««X«ar to C?|^} . Sf tlm e^OinSsr ia futdStitHi has ao ttoxnal 

^liiA ^!it3!« i8 X8» Mat l3iW in ^le 2 direetioa> bmoce etoatitm (^) 

fiini^tififlts to 



4 ^ ♦ ^ "^ Pe ^ (50) 



S&0 pf^M^^i #f iatcam^t Jd»^ 00€iar© ^^lian tJie 3^n i?eclK^ is at right 
m^m to its «i# of n^mmtscy^ {^m priiKslpal axte)^ t^ flguire li 
(fl^ la Ite srlBcl^ ii3Elis -veei^nr 

j^g la tfee «i5ie ^e^^iftd froi ipi^M C%*^) to fla» (%^i) 

(%^M) la tlie sOi^iie ocnon to ^ m& BM (etc 4 

f^rc^ t4ie la!ir of e^ij^s^ iii i^jterlcal t^igoncs»tey 

{^S ♦ (A)}* « {^ A ^0 % ^ Mm a Bin % mB f^^ {%.) 

Xn tM0 ^<itlim it ^UX l:>e tmmm^ is^t tte spl^ I0 fsMSt amt^ 
€^ (1^ ^Si^m% ^« If t&lB eo^li^^n I0 ^^t (a sii^i^ of <teokli3g 



* 77 * 
^^B oc^i^iitlim is is^^m^ in i^f « 6)^ mm t^ heat xutea ^n Isie 



1^ i^tiBg ^^ fmmimr m^mu 






n 



1^ ^t^ Ite ImB^ titim iM mm pg^ m^% area Is 

^m^ i% "^^ %) i# ^il^^iJilN^ mm^^ t£ t^ direct ^oOar fe^^ inpit 
@^C%) ^ ^t ^ (t&«#0eyLi® iO^i^^m c^?ti^»& 1»nip)* B^p^td^on (^) 



^)] 



* M2 * ^^^ % sIiifSq ^ 2 ^^0 %) ^ o>0*^tjg 



♦ % i ^(2 * wi % ^lm%0 ** S eos 



?9- 



m 






m §Q i t|l • mB 



%)} ♦ %< |Cfi • ©^ % tEUs^% - 2 eo« %)> 



IN ^ CN 



% « % < ^1 » ©®i^%) - 1(2 • «@s % sii^% - t eos Q^)) 



filter ^«]^3NLit #<p£^(Sii (^) iisei. iJSAa^prtitlJ^ 0^ ^r^er cms €^€iA &t 

f-Q fl^ is^bp^dueisji #fia!i^^ (3.9) it iM tsmi& 1^(t 



* agg oofi 2(6 <*> t)3» eoe Sth (55) 



«Qe * (t 



* do - 



m 



Hie 1»@ttt3. laeaai&x^ pmemr (1^ i*«3jLati<m) is 



««♦%♦% a Sa^(o®8 n/)^ -i^ {J« £ 



4' Sr^ % «os 6 eoe*(& - £)}[g5<^#%>] 



m 






-Bgg cos 8C® ♦ ♦)} 



- 81 . 



%(S) « <{^j>% • {j^ £ ♦ Br^ % ce® e ««»*(& • S))'(»u. ^^C^ ♦ ♦)) 



) « </^^% ♦ <^J^ £ ♦ lire % oas e «>s ♦(S - |)) {j^ 

• ^ ^s 2(© "^ t)) 



%imt is 



i«^ tlie net lieat <m a murfiauM «3,oaniat Is, t!ie&, 

* ^ IS ♦ *^ ♦ Tj>« ^ » ♦ jftt(&) ♦ fi(8)eos A ♦ f2(S)cos 2A 

♦ %(&)co6 U (59) 

<M9^ ft sBenr dbMomeeis etti0 mcsesfiaxy to prepare e<iaablo& (59} ^or its 



m 8S «* 






M0 -*» t/0 ® 



l^eaa set 



f * f^ {i + li # Ig ♦ .., 



j^^^«% 



TjSef^ e Q 



iQysiM. 



M?. 



% i 



3P* 



00 t^t eipatim (^) beceHsaes 






♦^{l ♦ in^ ♦ Hg ♦ 613^2 ^ ^ 






(%)» ♦ {«0(S) - <f0),J ♦ il(8)coa A 






"^gj^l^ 






<i>fg(5>iS9e A ♦ f]^(d)e9S hii (6l) 



i^d 



f!i*.a«4t.*3!M 



^ ^ ♦ ^ %ig ♦ ^ g^ « ^ ij^^ 



fde iKamoeffmww soiliatlmi (for tj^) is of ao istsreet sliKse it Is aot 

p»xlDtte* IKte porMooLar eolutioa of 1^ &m Ton twai& hy r mm mixm 

%l » fioC*) ♦ ^(t)oo« A ♦ eg(t}oos 2A ♦ gif(t)eo6 kA 



^ ♦ 3^ ao - I {%C«^> - <%>B.} 



gJ: ♦ (}^5 ♦ >^)^ « I fi(S) 



m& 



m 8% » 






gr" ♦ C>^ ♦ >^)% * i fki^) 



iSvere 



% • ?J ^ « -^^ ^J% * -^^ 


















*» 85 ** 



^(t * t)| n > 0» ^^n ^flstaM^ii {$&} iB iitAiifi l>^ 






Im^tAi^i^ ii^ti t% £^010^ lim^ 



1^ * ^ ^i • 






- 1 ^ *i^ 



^(m ||_ is B'^imsmS.i &£ -letM ^r@«y^ @t>s ^ ea% s^FtidUaet^ 



« in# s 



|j_* S ^ * ^ «s A ♦ .?^ «a:MS S^ ♦ 1* «sos JA ♦ ^ c»i>8 %A (6>) 



item 



[«o^*^*f*^] 






s% % ♦ % Sgji <% » 


1^^ ♦ago 62 t 82 g 


% «2 ♦ % %]s % « 


%- * ^ %. 





SkM/ agsalja^ tlM» haB>qg9ex»C9%te ac^titi<m of 1^ is Bot perioaio and 



^ 86 ^ 



m^ iMim0mi^ WL^ iMm ^m ^itmm^A ^fuaMi^ ^o^ Igt altar 









*^\'^'lh\ <65) 






^^ ' ^ 






8? 



* Of * 



cix\-r%).-k-^^^^^^ 



2 



iltetm % > So > %• 3to away «ita«!8 the «^@p:xxsiaatlati eeaa be aafie 

i^OM 1^ i0 a tliB« -wriiw* ^paaatltar and si aeasuree ^le space 
-meimm (inoftoe iwiins*). «i>e pare tAm ^srimee casa fee s^m^sosS.* 

i««wf»aw> * %C%)| i^ (cos A)fflaat - i 



«o tfanft 



H=(^)*<^ 



n 



tk i» «isi^ to prow iStm ttoe MBfiflft -walne of 1^ ^® **^*^' ®*' ^**®* **^ 






«8^ a OStsiirf ,IMQ£^«08 A 



C^s4^r,iaeaa)tt tr |C^Si4jrf ,b«x)j 



mS^ mm m0 ami t&m «f mmUm (^7) is 



c«.=%-lf§»*^^^) ^^' 



SI ia ewey caae iaefers ta» ojiearaUm 



(a)m - I / (2^)^* 



l^isMm (a) i« ia ®»o^ agreea^ot nith eipjatioa (25) and shows 

It0« Ills Mxm m$. fl^aee twosn^ratene variations eoffibioe to 






pit 



%,4 • ® =^ % « I J % ^ 2£ (%)j » ^^i%,a^^^j 






-\l/k 



^^•{l^ ^4'^*j -(%) 



iti aadt a^«itfi» ^e^c^ (^c^an I) 4t i»b altowi mi* 3^ Is *K&0 

i^m^k tte^ ti^ip®^t!iffi0 '^rerft^s "^tli tK>1:3bt ttoB and spa<^* 



* 90- 

tee. ^^m g% tB mBi3iimM to f^@«eet tte el#eterai^e efolisest £r3Q 
liirfM@@ mULi me* WI.B $sm^m m$^ (at Jbeest) dogrii^ #£ie ^l»itia. 

m is #'«Mii^:^ f^im ^ mmm^Lm tmM&m ^^eMm (63) ^ba^ mm 
tIEpsf aim® <if niwsh Q-^plpsiat «lll l3# a ftmoUoa of not caaXy the iieat 

n» ism m^mmm. Xf t^s f^«t is negHeeted ttte xesultlag 

UlEVOir fisem Isms cGf tSto CKetter €^ thet esiused t^ OBillitlng ^he 
i(|.M4c» Im»«Mi% «tfia&«t. Wsm^'me, if ao econauctive bea^ transf^ is 
(iMo tl30 fi^paiwtistil^) fioid on3y jrauSls^'ve tarazi^fser used t^been 
£l»citimU<sM CKf tlie spaceeroft's escteimal sur^etoe Is 
Of »& ernaS^ mmmwmBm to "^ne tx^ismeuL ^m^«v$^oaemB* Sade^ for 
4d|yi,« <i&ie the loiQl^rtlcal leraiblMi is x^dtoced to t^ sisBole issHs^fsa of 
ecaidug ^te s^srstM «^ o^pbtioos Sefised li^ e^s^jB^bimi (S6} . Shis t&ak 
IrI fiii9ia.illed 1^ anQtntgiisg «ftj<i,tiim (S5} over oasie orbital paee. !l!be 



iWKUJlt id & set of al®elm>ie etian^cais i^eh axig limsr iia %^ &o& 

mm \m mSLv^ la^ osrdineo^ m&Hba&s of aatrix aXgebsm. 



. 9a. - 



@f Ujm*&m^mSm^ tnq^raistisie ais^rilnxfeLs^ is gi-v^ below. %b» 
^^prtiet Df liitt ^lisier (tlie ni^i^l^) d^em ^ iUu»lr&te this 



l^iffli^ mmm^ mmSmm-^^ (l) * 0*155 m&/sd& in. % 
C^ltMm «te»al 4ifl\j©4vt% (a^) » 6.T?© Is.^Ma 

]toai«» ©f i^ii^w C^) « 15 SB. 

mm. w&^Ls^mrima oiisMiitr C^) * o.^ 

S|^ aso^ « IcMg tarn 

@k1»it v«iriQd I. » 100 «lii 

fla» ia iiir»ot maHli^t (%) « ^ adla 

1^ Hds «3tcaB|p!le> eoad fbr l^ asSm of saving lebor^, tbe eartti tlMaxmol 
yttOiatlim stid Ite ciUbeio Iwtat 19««» lM»»fi selected. Ibis is not oaaat 
to Istg^ ^bfit tlM^r ar« DegXigilalei ^ley axe 8i8q;>l^ seglected in this 
u XM&t i3mm &oeaS±is$joms e^!uati£m (60) r«»duees to 



% - ft) K>^ 



92 • 



***** *| «M» 



S ^ §.0^9® itn/tn*^ Mm 



^^teis 



<"(^MTr)f 



|§4)|0.^)(-^^^^y » 5^*5 X 1<^ 



€BP 



f* « ^88.5® B 



Q » i^ifl^j • 0.06^(0 .0979) (0.23.) (488 .5) mx/iM,^ 






^ « kl^\ « i,©gl62(Ma)*^ 



wsA 






^l^y» 



0»GgT 



133^ CH^ 



>^ « 0.05^2 ♦ 0.120^ * 0a566(Kla)-^ 
Tbe ^taiMi/^aadeaat foasUoas ia etmtloa (57) em gima liel©» 



k<Si) - (foM - s«g iofH . ^ 



Ife^c© B ie one in i^ ewnligljtt ctat a«?o itea ^ spacecrstft Is is 
das!e»es«* ^a& ooe£ltcl«ats of coa A eaad eoe &h in «q^tioa (?7) 
elasiaify t^ 






{%4%) * C%)^ ^ 0*0^ {a - 0*60} Btu/i^*2 ^sijji 

f^S^na 1^(4)1 i5C^)# m^ 15(^5* tl^« iremats is^^pt be i^«Hi dlr^otly 
t& ^^i^mite ^t|rA)^ ^lici^^ in ifemm^ is glutted m flpMfc 15(g) fc)^ 

A « 90^ 



- 95 - 

B^ @»agl«i is (^ jps>Meii3ar iatidrest aliK^ tbs |8!QpE»H^i> are 
r@€tlJL@M@ m^ ^llrts )je tb»^t %f imi "%pleal of 






Csy^ 2 ^^.f * ©.1^ X ^80.5 « ^^.5 * 26.5 « *^.2® B 



aiA if tte ^Sl# l#^ ^m.m mm m^^mm m&^mm^ vm vith t^ ^lind^ 

(ia WL& fr«ikl«iB|| tlm tte t«i|^«K«tasre of tto eXeetroaiee pa^«g@ 
omnOtd aei& one of «in» lemeds* Sf 1^ beitt ean^u^eeS to iSm el«etronic 

* 

of km.'f S» JtoMver^ if ^a %««6 wis transferred purely hy coaduc* 
tioHj «N« 'miim«m wou^^ e«^ «i teaieratore of '»60*2*' K. Zt is obvious 
^m&i 1^ ti«a|i«x«il»ix«i vBri&ticms smet be iir^esUiBatfi^ i» cases svtsh as 
^i». tf tisii @3^ i teiap»T&twe dvoj^ alioiit 1^ ie due to ti^e tisie 
tisn#mr«ti2l» mHriati^i USsm, ia tbis eitse ^aa» eirewf)»reQtieX variation 

Sd figwe lM$) it e«a be s«mh» HHa^ idiea tbe eg^Moeeraft enteics tbe 

ifRiiai#t tbe dUretuftKre^Mal t«i|M»xatuye imriatioos grov xt^idlr* f^^^ea 
tlie ^^aeeeraft eaters tbe emrtH's i^isdov m& teBq^rature differences 



2g ^KS U-imee^^imm |i*Ql)le®s of this %j»e sera <s»isaMJly sal-roi Is^ 
^ t^ a^»ilE%gr iee&i«wi ^»»i^ %^Cl "^ li) > :^^ tto £^ot@ in 



m p?e*tet»i lay t^ Uatur ^pg^esAiaKfeitm to f , as^ ®e»i83^11y gsoi, 
ffag Iji^g^dt fiart 4^ ^i ti9^|63ri^S£^ e»w mm& fwm. -^^ fact Mi&t 

M#i» :i^ ©mile e«8il^ m^iS^^^g W mm&sAt^L $33mm®Mm,, i&mt 

irfitfe ^^* ^^tewamit. ^at is %0 «ar, a&iwMmii ©f me liM«riaea 
v@^«^ weSh^ msBpe hisB^ ma^ Wm, Ib mmA.-^€» minUom Hmfu^ 

^ %♦%♦% mm iM el^str ©^aHIterim nith tli© 






P^a^ tl ^Pf^ ii^SQU^iii^ @i^C^Mi%iim^ 

Lji Wm^^i^m^^ hm% ll0¥ '^^ a ncmliB^tr 



-97* 






'^'®^-ii 



lam.% &mSm^'^&&. la ^e iii«eyi^s af i^be ^b«»3JL*s tsj^e;^ p2.aj^. Wim 

p?ii#@i^aies^ ^^ is ei^p«saed m> - 

X ta mmmxteS. in tto voorfaew aorsiaX dlz««itiem and is zero at Hbe 
insvOaf^ fsuee, ^tea iOkis eq^proacisaticai is sg^ied, etuaticai (X) 
mai^ltlwm to 1^ voU^lOMMm aifftaasifixi efoation in one space varifibble 



tHe baak f&oe <X « 0} is iosuisted, ^enee 



|S „ 0, X :- 



the £)ro»t fkM (X » r) 



.K g » Sot** - 4(t), X » T 
dX 



* 9S * 



|«C*) - C^J 






wj£ 



'Sliia eoipwsaicm vt2X be eatiell)»d at eeush canler of me^p^tuSa if 

%(t#X) » eoxist 






a%^ « (t)i 



fl^^ ^m mm^immt "i^mMmcf ^m^tlMk em l^ 0atiBfi#& ^ a asra-^i^ 



If ^^3^ ini^il tr^i^nt salmM^cm ia of n^ imtei^at i^n 



•*• 1@S * 






E^@ 






aii& ^dm^ IMm ^^s^p^gmtlim met ^dit tmc all t^ tbe^ 

m& m urn* lMMjiS:s^tx^ Wda limt etaatl<m 1^ 1 « ^ aad aMiiig 

to title fSMmer o^partl«% ^bm a£^mt acsae rearraa^iafttab, «id eetl^log 

9 









I^H^ ^i«mtljg %|(^^ i^E^^ its £«i^ ais£L ii^tgtoax^ psst^ it fbai^ws 
£^(X) » 1^ meh s^t em %X " %^ sisli qe^ X sia o^ X (7^) 

%^{X) » %;,j eofilt ^ X «Qifi ee^ X -f ^ eiji^ o^ X sis o^ X (t^) 



%(3(| <w w^ (% X cos <% X 
l^(X^ m Btsh % X sin % X 

it SnHJLmm 'isai If r / tl^aa 



^ 1^ * 



^ [%a %W ^ %tx %CX)] ooB not j (76) 



1^ a 00^3.0^ i^o^irJttt' i^iries^ i^s^ is 

and inlntteMUsg tisis aaaa effoaMc^ {76} into eqiuation (70) » It fte^cnfs 

* %» \^^^J ®''* "*^ " •in ***® '^ * ®la ®^ **^ ^^^ 

Xf IM.i misgsmmim t» eetpsmt)^ JLseI^ two parts (tlie eoeffioieots of 
sin s0% m& ism i^^, z^ep^tiipely) ttie tesulte eon be ^tRritten^ t& 

imM» fwm, m 



• 105 - 






■^ 



r '\ 



\k ^l^ 



)-{ 



Hm 



> Ct9l 






%^ 1^, Mgjf Ig mm «viaimt&& at I « r. Qiis mm^SMlm. 



«a,B a»a ijjg. 



%^ttt]f mm be esspms^S cub 



0f ©©rtisia trl^^wsetirle iimfeiMes 



46£^^^%,1P) * ♦ 2I (®^ cos 1301; ♦ 1^ sia ^t j 



<80) 



the Ideptieal aara 9f %C%yXh it Is ^^viQus mmt 
(79) «i^ tte s^s<»rl^ (a.) di^i^a to CS)| teme 






n /^ A 



San 



< 



/" '^ 



®2a 



> — S 






v_ Say 



@Q»s%B»te £t>r sOl tb@ f|.(t^£) w^ be fmswl ta a. siadlar 



Titftji » %(t,x) ♦ %(t,x) * %(t,x) ♦ ... 



Om Sa^p<MPtiaife f^*iir« &£ «W.& sca.\itloa ll©s to 11» faet that 
it <»Ha predlet 1^ teiagp«9ratazt» fluetrntioas of a IMck i^aia. 0tra@^i» 

1%i^«^»id^ it mm iiao fee aasd to ^mstiiy -^ asswiptloii aseeesai^ 

^^it«£eflt^ 5reswn@r esij te fmasa 1» tife toouudasr e<»ai* 
^jnfiitieas fm %(t,X) it e«ai ^ m&m 



(fi(t,X)J * (®» nfl^scsrlpt ffi aamtes 
m«9 eiaee ^iMi Mek. I^am it iasulatsa 

at * {tmr $01 %) (8t5 



t^ m^t,n 



:J^ ^^d dt . EtC^) J %(t,T)dt 



6e^2 f %^Ct,T)dt 



t*^'. - - l(|-J 



fl^ £r@a «tit as0«»ed soautitm it is cXe»s> th@t 



* 105 - 



(f ct,x))^ ^ % - ir^^j ^®5) 



fl^ wmm?i€ml mms0.e 0.'^mi h^-e Ijytostrtt^s tes^idratiird flm^i&eMGm 
^^Pf©s® gte ^iH Is «?^0tti»s is i iaaiOi tM^ sod iside of a 

«jCt) » 0»3 X 0.0i^96B ♦ 0,3 X O.0»^968 cos at Btu/ln.^ • aln 

(^xttular facQ^pesie^ of himt ^c^e (a) » 0.12^ rftdiea^aln 

paHoi (li) » :^ ttHm^im* Worn, team, eioatlcm (77) 

*l^0 • 1^.90 X 10*5 Btu/fflin • In.^ 
•3^2^ » l*t.90 X 10*5 Bfeu/nia . lo.^ 



• 106 . 



ml^ 



"i-ll-r 



LJl^^j «. x,Qkk6 T&sSmm/iM, 



fmm 's^mWm C^l 



8^ fla&% 



M^m 



fif^^ 



80 -^toli 



^^ « l|a „ 027.7 K i# 



&3f 



% - ^.^ a 



%l&i%^ » % X ©*9 X t- X IQC-^^ 



m 11.1©^ X lQr5 Bla/ia.^ «*B alii 
<3»l^ T w 1.0M*6 X a. » 1.0M*6 radiaae 

<»»i3i <e|. T » 1.5970 

«Ofi *\ ^ " 0.50^7 
sin % T » 0.86'>71 

%H » 1.5970 






lQ« ®^j^U.'m {19} #.^« 

I^s^ffi %<^mMmm C7^) nt (7^) it tciilxsim ^Sm& 

gl3^(t) « 151.71 ^C@| » 56,1?^ 

ami, txwt ttm 89iipllifi^tiieH& ^ e^fuatioia (7S) 

%(t,T) » a.^ sio at ♦ 15a. .2 eo« at 
f^(t,0) » loe.s 8in ot ♦ 56.2 COS at 

fl8(t,ir) « 11,659.6 ♦ 1,617.8 sia 0Jt ♦ 11,2011.7 coo sot 

-35.5 X 10-^ cos 0Jt 

St is ms^ to iK»e Vbub^ isim eoaasteaxt part of •££Gi^%^(t,t) 

^^voiltsisoft & "WiwtiWt i^utif^ e^^aal to 

*5*«w X 10 W9 vO « 



- 108 - 
fg(tt^) *» *35*> * IS*^ ^^te »t * 1*1 mn iat 

1^^ ^^ ^^iQp^ir^iii'# c^ ^^110 Iji0ul^'feed face bitiS ^li^^ii;)^ l3@if$jf 
aaMal^ m a^mat^^m ^t mmBimA ta^ei^tire tfe^^^^to^t i^ rtitll*t 



- 109 - 

Wm mluMmk % 4 % ri@e@ mil e^Ksm tULs 'm.-m end Is t^»it3?e£9ic@ 

cIsiaBai' 1» i^ie^". a© im.-&u.mk % ♦ % ♦ % fsaia^ 4«»t i^iert ctf 
-te» '^ifftr llffilt @s^ ^ is mis @^ee (%♦%♦%) ii» d better 



^ « 6fts % - AEatA^ (S^) 



m « 0TA> SA^ a^ . ^^A^ 



S^ - (^)<%^ - %'> <^5) 



SL^ » fl2J\dt 

« If « 1> \prcj 



^ lio * 



lAilfib iM^fgt^s^B t0 






-^ 



* ta^^ 



% 



% 






t 



(86) 



Xf t^ 0iffi iloes iiK>% Isest tile p}^:!^ 1S3»a ttos e^^gmtlgiak ^fM.i^ 






^&l0 ^3^ ^ |£^^$gl%%^€. 1^ pi^0v4l^ 



mSnw 



Wi^ ^aHqy 



^01 Vw 



(8?) 



'9ar tilMk pc^rtia^&ticMEi s«»IuU<hi of e^mAltm (S^), it 1b sssused ti»Et 



«A-%*\*%* — 



tess^^ 



^a" • %^ ♦ ^%\ ♦ X^^ * ^AoX^ * ••' 



Itoa tbi0 a^si^ss^j^icm ta Intrc^eefi into e^mtion (85) it in ftnmd 



« l^S^lfA^^ 




m&f m WBm^^ tiii@ eaa bt s@|i®rated ijarto 



1% * ^%^&)^% * ^* %.^**^ * ialtlal €<»jai1^Q» 



m 






%*%*«/5g^*«Ag* •• 



© 



ii\@*?Aj_*%* '•• ♦i-^i 



£0 \ 



V * ^A,''^ ♦ X^A, 



♦^%%%^* -. 



low, let T^ » fA(0) ^ -©mt 



kx * ^%^(^)% « -(ic)%^i %<®> " 







and 



''^ ♦ '«'*'(Pc)% • -*Ao^(^ V» %«•' - » 



Ht^ ite aeeoi^pj^^di^ aolutimi© 



i^iirw ii giwii 1:^ 

f A(t) 2: f^ 4^ T^ 4^ f^ (89) 



- U3 - 



m^^s^ #i|W^^}@ C^l ®i^ (87) > tffiA ^e i«o^€GKlfflftte $6yLi3^l.<mj> 
e^mtMm i^) m& C@9)* B» ]^Q!P«Ei^s of -^e Yi^ileXe tieed to 

iMB m^0M em ^im smm m tlioee f^r ^le bo^ ui^ is ^^ 

& fipiife 1?C&) Ite liemUws ear«e, firm 35^ B to tl» eioiUb. 
fi«a *«^p@i®tu3pe, 555® t# is iBPefi^trted* fMs r<gpr«8i^Bfts tfce ease 
^ & 1M» mUjsA €^31s^^ &piii»^iig s^Hmt its mtLs of ^mmts^- 
Bus testis^ mmm is ^be ^m iSii^ aees 1^ 0irli»^^ larcmiaMj^* 
laitlaiay, mm sfOiaa^ £»s b©€a <aseaed to ^5® B aat mm ^y«eted 
t3 ii£««rt ti^iil^. 

1&© carw a«Bt»d (ta^ * 3!/^ ♦ SAg) is ^aaa to be ia good en^e&ei* 

nitll tto «es©t aslteliim* Tbs curve aaarJosd (f^o ♦ t%) 

tt» {te lljaeairlflehl aolutioa &e& ^aee not itroviae a, mxy 
Xn fifEve X7(a) the i^UncU^ lu»» l30@a eixSieiay 
Miteit fit<m tilt 6tii| a^ tbe cooking curves {tvtm ^^ B) ax« siteoim. 
Ag befoa»ii tbd mnm imelm& {f^^ ♦ ^% * %^ ^® ^ «"»** Isetter 
ttgartMnmt idt^ tlie esmet soIixUon idiaa is t^ curve marIsM (S'/^^ ♦ f/y^) . 
1% flurti adiing ^le tem ^ aliaost doi^aeB the range of e^paieaMXitsr. 
ia^boa#i ax» positi'TO &tat»saeiit i^iould txs nade from tbsee remits, 
n®xm ITCa) «a®gi»0t& «»at (f^ ♦ ^Al ♦ %J «^* ^ '*«^'^ *»*• varia^ 
tii^ius €^ Sa ^ to «i»oat 2^ pereeirt <^ H/^* 

Ito perioOie CK3Cliitioii« ttiis varieoioe is ebovs and lielev %> 
8zi4 tese tliis ease^ tte £S>»pe^ra»xt -varistioa coir repreaesta a ^percent 
'mseisMmt* fbds raii@e «3cr variaiK^ ia usuaU^ suffiei<(mt for 1^ 
max ilaaigii odf a|««acraft* 






it, M j%p%iai^ tt ^i@ j^euisite ^^tesisi S&sipt &t 

a, 

prtiricAialar pwAinitid ^s^ptMrnm by nsas^ of a Blaoxt Siseussicm of 

««e i^ftftiiae B^B^smmeaoi to aislil«i« teasi>(»mti£re oe^t;xtkI ty a passive 



^01011 of a t^«al E^cecraft sdj^t be Q/eec3«^i8hed 
in Ite feaiotiing woawr. Mx9t <mB isvestigatea ttie spin character* 
l«Um @t the ^aeaeran. Zf ttte nehieXe bas t«o &pija msdsB, as 
ppr«loui3.r iMatl€me4jr tltsm it is foite loraboble t^bn6 cml;^ tbe "icoag 
team wj^ tmoSe" neeie to be eocusiaered at tbis eteti^. 

*&e j^ro^eetted soma of tbe epccoecrstft^ refet&ae&di to liie Icmg 
teim S|^ @aei3^ ^li^uld be awrsged &vev one cyeXe of Bpin. 

file fmietlms \i{n} mi ^(n) eaia be coXouXated fear ewry 
mH^mnai^ me^tm of tte ^piojeecraft. '!^la ailove for tbe oaXoulation 



S{^j> 1^10^ ^s^o^d b^ t&i^f^ ^£t%'3^u% tf^if^i^tHTO c^iiiS£t«l€!i^ 

Wm »« lMi»a*»?e^ of at least cms of tha a^t^^raeO. mir^s^s^ 

iMiii le^ to tiii M#00t i^ liTOefe trap^iutofe lewis ia ^ 
Sn^^fnaO. slrmt^^^f^ m^ tm^ i^ ^aefarmdca seetioaii* If iKha ids#i^ 
l^i^ii!^ ^yg^t ^ikm 0sm.m^m£% wm^^^^mB In orper^tlCTi for 1mm w^wto^ 
#f ttoe it nfill in gs^E»r^ *»# ii^poEaiblt to predlet^ belbTO lamsdte^ 

id^t fee rn^tm^.. mm^ etmtloii (5^) U^Mately laads tte 

1*^ Mgpte^t mm 1»®em'te»e0 tl^ ocmditims are: 



~ ^ 1*00 
I ^ 0*0 



M* £%WBt glmm^ tt i^^gprart ^m% t 01101^1^ }m i;@r4>| but^ ts^er iMm 
mm^Wm it i$ lU^pos^l^^^ 1^ i^cMain^ 100 perc^^it Wm in wm^lj^ 

BWiX pefi^ts C%^) t^ filial ^M%^* 

Ite ii^ S.ai^^% wm^ im^mm^mmBg ^gse ^rar^M^ma are 

^ m Mi € u Q 

(a^/^) l^r Ite SM ^^ti§^« I& @^i^al ^yb^re is ^ »#iif*^^^ 

§^2 t@ 0#S «^ umiall^ a^eift^la# It Mimild be rmm^i^^^ Mm 
^m% ^^ teii^^iiaal mm {l^m^t i^acliafe^a lt»r e^aMiOe) can alter 

i^te^r or iK>t a pa^^i^ la^sarayg^ ecmt^*^ 0i^b0« is possible * If it 
1© tmt poasibJ^ to a«M^w ^^ pmpei^ ta^pei^tim^a bgr a passim 
s^^i^^ief it 0l»ald atill be towlc^ped aa far m ^a^ble uiMm tfeis 
^^dUa iTOS^i ^^ a»aMa m^ 01^ t4^ atstiw ittieriml eo^Ets^^ i^pjfaratoia* 



^ 117 - 

fBm^B nmx 1m l^^^jy^d* ll^m Olstrlbwi&ic^a^ ref^^ t^ ^^ ^^^^te ^^^^ nw^ 
m^tijm iB mm^m& to ^ isolated f^i^tm its i^j^g^teg^ m^ wm te 4$ml^ 
isiili^l^ ^ the 3»^^as p-^se^t^ 1b tbla la^sls • M €^^|4ia^^ of 

a^iMi^]^ 0irfa^0* ®ie pre^cmsl^ ^ai^ositi soautio^ bh^ ^t ;^^d 

%^^ a#o1d€^^ ^ ^li ^mm^m£% B)m^& be dividiid item mSMm ^^ 
s^rt^^ ^ ^^^tioi^ tjrtx^ftue^a 1^ efoatlcm (26) • ^0MLs ^|p?t*adht 

^^il^* stle^ti^ erf %^|^ ai^ % v^vmn w^ m^^ mk Wm 

m£a$i^ S&mia ^i@ apac^igim:^ faaw tw> spin bk^3#b^ I^i^^ *te cteali^^lJs 
taii^i»t\»e© €^13^ be acMe^^ tort^ tiie s^tort^tiae sgi^ m^ fey 



* 118 * 
A ftew of tte ]^0bl^as ^h±&SL wAm to lite la^CT^ iesl^ of 
'^ a lt»E» aip!tM«^<mt Qils^ ti^oartama^l^ji ^ta tto^ iK^ieilimar 
mM.M IteMs % ^ % ^rsr^^pcmaa a^motlr t^ *^ li»ia3?ljiaA wlm»^ 

1^ mi^s^ri^l ^^ntigLea p^i^ntad iM tMs l^sia i^if^ ^i^saia 
1^<M»© l^bs^ prtwsriay ^^Msi® i^^^^rtimn pei^lar 11^0 ^e 

for Iteree m^^B c^cmmM&^ ^ncmirt^mM. iM tte iiiextial desigiBi of 



* 119 - 
^^ii^€in^« ffeis ftrit oBm occurs lAan tj^ ** space s^^a t^^ra^tertt,** 

W^ mmmdi mm iM^mmti^^^ in ^i^ of a i^p^i^sarajft ^t& ^dm 
t0 t^ ^€eei m^r iM tt» ^ai^ ^^^l^lea^ first ot^T ia ^te ttoe 

i^aa %B wmM^ Sii0 %fe of teat Hou is ^ma:M4 Iss^ ^m "mlX^immn 

^^^ in ^il0 theai® la ^m^aed to \m ^tt\im* 

Ste ppolbtlem of cileylatli:^ projected m^^m of a^^i^^^^isiit ia 
al;*i^^©4 te section 0* ^m projeetet ar^a fc^ a mmi^ wti^ m^ 

it0 aicl0 of ^^^tr^f I aM for t^ mm^ ^imiing ^ik:)^ aa ^^dla iDomal 
t^ tto^ «i^ of sy^^efeey* It is 0ta;ted lu tWU ^etl<^ ttefe tlte 
0C^«^0 aa»a pEmJeetloip^ <^aii be ar^pres^nted by fcm^riler eoslm aeries* 

]to sectic^ iD> the aabedo ^^ai ^b^^ therMl #i:^rg;y> ineidi^iat 
cm a ^pmmormSt of asi^ili^ary ali^ji is ealoid^al^^ 'by ^^ t^ of a 



- 120 • 
"i^^^c^sHU^ ^^sluf^ i^g^a0# W^ p^^0tsS af*iNa ojf tte ai^i^s^i^g'^ 'bo^ 

Ite ^^tarttli tteiiM^ €Ki^i^ lBcJL^ir& ^^ i^ i^liii^#« 

tlcm m^^B mn glvtn to aid %im wmSmw ia 'd.^iaJli^^ a Mgrn^mmm^H 
mMmk w^a^MMm 1m tite i^m w^ i^ e^rtb. 

gifm f» tt© sfi««®p«ft*s teat '^rsnetf^. It is pds«e4 Uttfe th^ 
Mds i^^Mi of «<paticHW t2m;^aiy aretoli^s Istegrstlaa by ^tlgitaO. 
«K»piters SDdf la i^SHi <!a»»s viK»i« larg^ teaagpeztttuxt! 



'&&» aoffUon p?<e8«iiit»i a sl^qOift^d etu% of al1»edo aad eeorth 
l3»<diifiigjr on «a arbitrarily ttbei)ed spacecraft ^ vM.dBk elecerly points 
out i^ift sH&at isfiDQoa^tiuatt 'vai'1^2il6@ cacsBoieetied vitJi he&t traxisfsir 

l»it«(iea» tl» cnhtUi aad tiie epaoecsmft. Al60> a» eatj^sessloai is 
«totiiliw»d tiliidtt eim 1)9 liuwS to eaXouX&te t^ a-^rage e<|tiUll»liim 
ta^^exmtaire Askt ooy istoCLated secUcm of ^» spaceoxoft* 

A 3Wtbod uae£^ f<»r sea^viDg acoalimax- differEanMal e<peiticais 
le giwB in Metics^ H. Btis rae^iod is iatro^bocaed by ctee^aaU^ tli&t 



M mW^mi t^ m ^ilirtl<» f^ th^ tai^ratm^ time Met^^y ^f it 

"^Mk^ 0y^WM ^hit TOdTWsll^i. tffl^t^raliiiife fluetiiat^d^is is ali^ fm&SL* 

i^m^m^ mSL m^B^m (^m^m^m^w^e) fiLu<Hmaticms iM m^i&a J. It la 
0©tdKLti^*^ia fr«t ^^10 TOlutlo^ «mt ham tte ta^i^ral «A 0]^^^ ^t^m^r^ 

ftngfljly^ it it 0te)^m h0^ tte t^ffleratuiiis of a bc^^ eis^^s^ toy a 00<»i^ 

la^ firtt 1K^ t0 i»mBl^T^A to tiie m^^nd boflgr* WLb Xm% tmt atoire 

its el^^ft^c lec&aj^ eaii be csa^tilated ^tm^t msm teo^eclf© of 

mm prrte^to^tii^ mttoA^ vum& Ib tMi ti:^0ii^^ t& mUm Ite HEmllJsear 
^ISte3E^iitiai ai!|u^*icii0, U usM to q^bt^m tte ^ilutdlcm of % lii«» 



- 122 - 

aU^rtntial e#»tioii with imtiiSxmm \mm&B3cf mmM.Ujm^ (in tee^^cm lO^ 
^Im «fttol ii ^ii0i:ml^ lix ita na-teire> and eau l^ ui^a to s^i^ swi^ 
o'^b^ ^mUB«r fi*^ia^. Its Jmln useftilx^as lie^ in '^^ fa^ IStefe 

tC3ll^ %• it. 

0^iwj a^WBd ill /Qil0 M^0l0* It l0 i^^saary that tfee 

p^^cstf* of tiS0 pert^lsatiism ^^3oa Mm "bBmi mt^iSBhM Mm* fbt mm^xi* 
<^ ^ewiipto #-^11 to seeMbOUt t stag^sta that tte partuf^^felcm im^y&& 
m^W^ ^mm^ m3^mxtm^ of 



%it^o 



WUmS^i aeetion If outXinee aa asproaidb to tiie prtMim o£ iS»wm3L 

8^ IUJi«a»s»d £{i ^3is ti)0®is. fm eKannae^ the peoWjm of BsattiOe 
If <»>e is |jitm«@t«d IQ tills pr^iiaesi, be elsould oemsuXt xieltejfeQoe 5. 
raaiofetim coefflelcaats (Bjt^^) aara Iselag calcMlated. 



toptl^r ]^roblCTt cmmwa^ ^nomm^T^d %ja thearwo. ^^J^ m^ tmt 
sowr^ ii^ra, %b i3^ M^ re0i0taiK^ to coBdtocrti'^ b^at fXm at -tti^ 
4tB^ti^^3^ betimea tw> boQies* If t^ bodies »*6 MLd t^^iai^3r fey 
iBterfjs^^ eo^Aset p^esure only tl^^ th^ir <K^i3^m 1>oxmaaf:^ "lilijr la 

m4© itf teat l^ai^fer lairough i^se tmterfeeaa la ^t mil -mM^^W^ 

M^tallj* 0nfc^r^2imt^Jljr^ such e^g«l»mtal ^ta a^ imrellatol^ 
be^aisa of flai^ lic^tt^r aM the ge»ria ijmbili^ "^ wpn^nee #3s^^^ 
«^nt^ refult^. "Bm ufual ^etb(^ of avc^idtisg sueh iirt^rf^^ ^^^^^utl^rn 
tB to r00ort to ^^^aii]^ m: boMii3^ tecamique0» fh^ silit^m gr^aae 
tia#4 f^r *M|ti ^^a^mm* ^j^lications cmx Blm te used to grea;tly re&iee 
lEterfac^ ^Biataii« to heat tlm* Ifeterfa^^ i^asistMie!^ ^ mm^t^tm 
lii^t fXi^ ns^t l^ <x^Eisl#^0d "^fey^ dl.®Cls^li^ tte ^^futootl*^ tei^ 



tort tla@ M@td3^«B @lmm in It^uc^e i3(a) ^tetni# iBifh eaA «& 
jfe-i* M^rr SM.m ttB^mm&i. fbr twXtmtlUag ^to all^nio i3e^mi^m^s» 

Wsi ^GEltDsr also ili^iss im &^g^mm Me n^-Utuis ta !li%.%sa^Uie 

m aim irlstee td tbeak las'. JeiaeB B. mglm, h»e& of 1^ ik^rospaec 

Biagl»ettxliig Ssfortaant f«r Ma m&vl<se, patieiKsej sad apea nina ds^edjag 
tHe ppepartttitm of tMe iteisis. 



1» MI^0jF A» !♦: ^m ®fflperat«e ^f an Qrbltl^ MlasH^* Wm&^Bu 
fep. Ite* aD-*^ (C0ia*raet lo* SA*©^*^^^d l8>. Jet l^ofiilsi^e 

S* Mug^ltl^i B« Q^p aM aU^DX^^ D* M» €•: 1^ Bff#^ of tte &r&^s 
mim'^&mBB tm tim Cferbit of a Stem* SateHi-tosi* fe<ai. lo^ ®^* 
©*W» %T5# Brttiik l.A*!*, Oiet. X95T* 

Sat^i21it@^ Fart I. Wmm ^^ fStefi^ to 3&i^]^^ytiaM^Qt« ^#1^eal 
Bo^ IKI56O1 hm§lw Bmmmt^ tSm^m:. 

Sy^Pl^^sMtt H> WmliMm^ l^m£l%B fmt tM l^trtod M«^ 3jr 1^3# 
Itetm^ M^ 26^ 1S^3, lASA M X*^^^ Im^mf Mmm^ C^n^^r, 1963* 

liiait& B^^es Su)>4^c1^d to &ilar Badiaticm in ltaimw]^mm^iXf 
Qprnm^ Ifectoleal fel^ B*^, I<e^^ Itee^ar^ Center ^ 1961* 



« 126 • 

1^ ^il^r^a tilt f Ir^iiiia I^i^Ljrt^i^dle ^^tlt^tte ^ Mf^ ttuiilea 
i^M temsHt erf Mant^ of Science in 



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Figure 2.- Sketch relating a cone to a viewer (v) . 



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Figure 5»- Sketch showing the relation between t)^ r]ny and ? 



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